P. Dankelmann , Y. Guo , E.J. Rivett-Carnac , L. Volkmann
{"title":"The oriented diameter of graphs derived from other graphs","authors":"P. Dankelmann , Y. Guo , E.J. Rivett-Carnac , L. Volkmann","doi":"10.1016/j.disc.2025.114443","DOIUrl":"10.1016/j.disc.2025.114443","url":null,"abstract":"<div><div>The diameter of a strong digraph or connected graph is the largest of the distances between its vertices. An orientation of an undirected graph <em>G</em> is a digraph obtained from <em>G</em> by assigning a direction to each edge. An orientation is said to be strong if the digraph is strongly connected. The oriented diameter of a graph <em>G</em> is the minimum diameter amongst all strong orientations of <em>G</em>. In this paper we give bounds on the oriented diameter of two graphs derived from a given graph: the complement and the line graph. We give bounds on the oriented diameter of the complement of a graph <em>G</em> in terms of the diameter of <em>G</em> and in terms of the oriented diameter of <em>G</em>. As a corollary, we obtain Nordhaus-Gaddum type results for the oriented diameter. We prove that the oriented diameter of the line graph of a graph <em>G</em> cannot exceed the oriented diameter of <em>G</em> by more than 1, and that it is at least, approximately, the square root of the oriented diameter of <em>G</em>. We show that both results, in some sense, are best possible.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114443"},"PeriodicalIF":0.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A characterization on (g,f)-parity orientations","authors":"Xinxin Ma, Hongliang Lu","doi":"10.1016/j.disc.2025.114440","DOIUrl":"10.1016/j.disc.2025.114440","url":null,"abstract":"<div><div>Let <em>G</em> be a graph and <span><math><mi>g</mi><mo>,</mo><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>N</mi></mrow></msup></math></span> be two functions such that <span><math><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≤</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mtext>and</mtext><mspace></mspace><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≡</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>2</mn><mo>)</mo><mspace></mspace><mtext>for every</mtext><mspace></mspace><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. An orientation <em>O</em> of <em>G</em> is called a <span><math><mo>(</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span>-parity orientation if <span><math><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≤</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>v</mi><mo>)</mo><mo>≤</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> and <span><math><mi>g</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≡</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>v</mi><mo>)</mo><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>2</mn><mo>)</mo></math></span> for every <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. In this paper, we give a Tutte-type characterization for a graph to have a <span><math><mo>(</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span>-parity orientation.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114440"},"PeriodicalIF":0.7,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143428031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An extension of Pólya's enumeration theorem","authors":"Xiongfeng Zhan, Xueyi Huang","doi":"10.1016/j.disc.2025.114445","DOIUrl":"10.1016/j.disc.2025.114445","url":null,"abstract":"<div><div>In combinatorics, Pólya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds. In this paper, we present an extension of Pólya's Enumeration Theorem. As an application, we derive a formula that expresses the <em>n</em>-th elementary symmetric polynomial in <em>m</em> indeterminates (where <span><math><mi>n</mi><mo>≤</mo><mi>m</mi></math></span>) as a variant of the cycle index polynomial of the symmetric group <span><math><mrow><mi>Sym</mi></mrow><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. This result resolves a problem posed by Amdeberhan in 2012.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114445"},"PeriodicalIF":0.7,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A combinatorial proof of a family of truncated identities for the partition function","authors":"Yongqiang Chen, Olivia X.M. Yao","doi":"10.1016/j.disc.2025.114434","DOIUrl":"10.1016/j.disc.2025.114434","url":null,"abstract":"<div><div>In 2012, Andrews and Merca proved a truncated partition identity by studying the truncated series of Euler's pentagonal number theorem. Andrews and Merca's work has opened up a new study on truncated theta series and a number of results on truncated theta series have been proved in the past decade. Recently, Xia, Yee and Zhao proved a new truncated partition identity by taking different truncated series than the one chosen by Andrews and Merca. Very recently, Yao proved a new truncated identity on Euler's pentagonal number theorem. The identity is equivalent to a family of truncated identities for the partition function which involves the results proved by Andrew-Merca, and Xia-Yee-Zhao. In this paper, we provide a purely combinatorial proof of the family of truncated identities for the partition function. In particular, we answer a question on combinatorial proofs of two partition identities, which were posed by Wang and Xiao.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114434"},"PeriodicalIF":0.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New MDS codes of non-GRS type and NMDS codes","authors":"Yujie Zhi, Shixin Zhu","doi":"10.1016/j.disc.2025.114436","DOIUrl":"10.1016/j.disc.2025.114436","url":null,"abstract":"<div><div>Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be MDS or NMDS. Additionally, we employ the well-known Schur method to demonstrate that they are non-equivalent to generalized Reed-Solomon codes.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114436"},"PeriodicalIF":0.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Wilf classes for weak ascent sequences avoiding a pair or triple of length-3 patterns","authors":"David Callan , Toufik Mansour","doi":"10.1016/j.disc.2025.114438","DOIUrl":"10.1016/j.disc.2025.114438","url":null,"abstract":"<div><div>A <em>weak ascent sequence</em> is a word <span><math><mi>π</mi><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> over the set of nonnegative integers such that <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span> and <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≤</mo><mn>1</mn><mo>+</mo><mrow><mtext>weak</mtext><mi>_</mi><mtext>asc</mtext></mrow><mo>(</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></math></span> for <span><math><mi>i</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi></math></span>, where <span><math><mrow><mtext>weak</mtext><mi>_</mi><mtext>asc</mtext></mrow><mo>(</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></math></span> is the number of <em>weak ascents</em> in the word <span><math><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⋯</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, that is, the number of two-entry factors <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> such that <span><math><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>π</mi></mrow><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span>. Here we obtain some enumerative results for weak ascent sequences avoiding a set of two or three 3-letter patterns, leading to a conjecture for the number of Wilf equivalence classes for weak ascent sequences avoiding a pair (respectively, triple) of 3-letter patterns. The main tool is the use of generating trees. Some cases are treated using bijective methods.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114438"},"PeriodicalIF":0.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on the multicolour version of the Erdős-Hajnal conjecture","authors":"Maria Axenovich, Lea Weber","doi":"10.1016/j.disc.2025.114437","DOIUrl":"10.1016/j.disc.2025.114437","url":null,"abstract":"<div><div>Informally, the multicolour version of the Erdős-Hajnal conjecture (shortly EH-conjecture) asserts that if a sufficiently large host clique on <em>n</em> vertices is edge-coloured avoiding a copy of some fixed edge-coloured clique, then there is a large homogeneous set of size <span><math><msup><mrow><mi>n</mi></mrow><mrow><mi>β</mi></mrow></msup></math></span> for some positive <em>β</em>, where a set of vertices is homogeneous if it does not induce all the colours. This conjecture, if true, claims that imposing local conditions on edge-partitions of cliques results in a global structural consequence such as a large homogeneous set, a set avoiding all edges of some part. While this conjecture attracted a lot of attention, it is still open even for two colours.</div><div>In this note, we reduce the multicolour version of the EH-conjecture to the case when the number of colours used in a host clique is either the same as in the forbidden pattern or one more. We exhibit a non-monotonicity behaviour of homogeneous sets in coloured cliques with forbidden patterns by showing that allowing an extra colour in the host graph could actually decrease the size of a largest homogeneous set.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114437"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enumerating alternating-runs with sign in Type A and Type B Coxeter groups","authors":"Hiranya Kishore Dey , Sivaramakrishnan Sivasubramanian","doi":"10.1016/j.disc.2025.114439","DOIUrl":"10.1016/j.disc.2025.114439","url":null,"abstract":"<div><div>We enumerate alternating runs in the alternating group <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⊆</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. This leads us to enumerate the bivariate peak and valley polynomial with sign taken into account. We prove an exact formula for this signed enumerator in <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and show that this polynomial depends on the value of <span><math><mi>n</mi><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span>. If <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> is the polynomial enumerating alternating runs in <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, Wilf showed that <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></math></span> divides <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and determined the exponent of <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></math></span> that divides <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. Let <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>(</mo><mi>t</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>(</mo><mi>t</mi><mo>)</mo></math></span> be the polynomials enumerating alternating runs in <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> respectively. By finding the exponent of <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>t</mi><mo>)</mo></math></span> that divides <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, we refine Wilfs result when <span><math><mi>n</mi><mo>≡</mo><mn>2</mn><mo>,</mo><mn>3</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span>. When <span><math><mi>n</mi><mo>≡</mo><mn>0</mn><mo>,</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>4</mn><mo>)</mo></math></span>, we show that the exponent is one short of what Wilf obtains.</div><div>As applications of our results, we get moment type identities involving the coefficients of <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, refinements to enumerating alternating and unimodal permutations in <span><math><msub><mrow><mi>A</","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114439"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the complement of a signed graph","authors":"Matteo Cavaleri, Alfredo Donno, Stefano Spessato","doi":"10.1016/j.disc.2025.114433","DOIUrl":"10.1016/j.disc.2025.114433","url":null,"abstract":"<div><div>Given a signed graph <span><math><mo>(</mo><mi>Γ</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span> and a spanning tree of Γ, we define pseudo-potentials on Γ, which coincide with usual potential functions in the balanced case. Using a pseudo-potential, we are able to define a signature on the complement <span><math><msup><mrow><mi>Γ</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> of Γ, in such a way that the signed complete graph obtained by taking the union of Γ and <span><math><msup><mrow><mi>Γ</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> is stable under switching equivalence, and providing a solution to an open problem in the literature of signed graphs. Then, we introduce three new notions of signed regularity, we characterize them in terms of the adjacency matrix of <span><math><mo>(</mo><mi>Γ</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span>, and we show that under such regularity hypotheses the spectrum of the signed complete graph can be described in terms of the spectra of <span><math><mo>(</mo><mi>Γ</mi><mo>,</mo><mi>σ</mi><mo>)</mo></math></span> and of its signed complement. As an application of our machinery, we define a signed version of a generalization of the classical NEPS of graphs, whose signature is stable under switching equivalence. In particular, this construction allows to give a switching stable definition of the lexicographic product of signed graphs, for which the spectrum is explicitly determined in the regular case.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114433"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral bipartite Turán problems on linear hypergraphs","authors":"Chuan-Ming She , Yi-Zheng Fan , Liying Kang","doi":"10.1016/j.disc.2025.114435","DOIUrl":"10.1016/j.disc.2025.114435","url":null,"abstract":"<div><div>Let <em>F</em> be a graph, and let <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>F</mi><mo>)</mo></math></span> be the class of <em>r</em>-uniform Berge-<em>F</em> hypergraphs. In this paper, we establish a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure through walks. Based on the relationship, we give a spectral asymptotic bound for <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>-free linear <em>r</em>-uniform hypergraphs and upper bounds for the spectral radii of <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>t</mi></mrow></msub><mo>)</mo></math></span>-free or <span><math><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub><mo>)</mo><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo><mo>}</mo></math></span>-free linear <em>r</em>-uniform hypergraphs, where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> are respectively the triangle and the complete bipartite graph with one part having <em>s</em> vertices and the other part having <em>t</em> vertices. Our work implies an upper bound for the number of edges of <span><math><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub><mo>)</mo><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo><mo>}</mo></math></span>-free linear <em>r</em>-uniform hypergraphs and extends some of the existing research on (spectral) extremal problems of hypergraphs.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 6","pages":"Article 114435"},"PeriodicalIF":0.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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