数学最新文献

{"title":"Monadic ortholattices: completions and duality","authors":"John Harding,&nbsp;Joseph McDonald,&nbsp;Miguel Peinado","doi":"10.1007/s00012-025-00889-5","DOIUrl":"10.1007/s00012-025-00889-5","url":null,"abstract":"<div><p>We show that the variety of monadic ortholattices is closed under MacNeille and canonical completions. In each case, the completion of <i>L</i> is obtained by forming an associated dual space <i>X</i> that is a monadic orthoframe. This is a set with an orthogonality relation and an additional binary relation satisfying certain conditions. For the MacNeille completion, <i>X</i> is formed from the non-zero elements of <i>L</i>, and for the canonical completion, <i>X</i> is formed from the proper filters of <i>L</i>. The corresponding completion of <i>L</i> is then obtained as the ortholattice of bi-orthogonally closed subsets of <i>X</i> with an additional operation defined through the binary relation of <i>X</i>. With the introduction of a suitable topology on an orthoframe, as was done by Goldblatt and Bimbó, we obtain a dual adjunction between the categories of monadic ortholattices and monadic orthospaces. A restriction of this dual adjunction provides a dual equivalence.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On bipartite graphs with the minimum number of spanning trees","authors":"Shicai Gong,&nbsp;Yue Xu,&nbsp;Peng Zou,&nbsp;Jiaxin Wang","doi":"10.1016/j.disc.2025.114514","DOIUrl":"10.1016/j.disc.2025.114514","url":null,"abstract":"<div><div>The collection of all (simple and connected) bipartite graphs with cyclomatic number <em>ω</em> is denoted by <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span>. We use <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>a</mi><mo>;</mo><mi>b</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span> to denote the graph obtained from the complete bipartite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msub></math></span> by removing <span><math><mi>a</mi><mo>−</mo><mi>c</mi></math></span> edges that are all connected to the same vertex of degree <em>a</em>, here <span><math><mi>a</mi><mo>,</mo><mi>b</mi></math></span> and <em>c</em> are integers with <span><math><mn>2</mn><mo>≤</mo><mi>c</mi><mo>&lt;</mo><mi>a</mi><mo>≤</mo><mi>b</mi></math></span>. The term <span><math><mi>S</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> denotes the skeleton of the graph <em>G</em>, which is defined as the largest induced subgraph of <em>G</em> that contains no pendant vertices.</div><div>In this paper, we investigate the problem of characterizing the graphs within <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span> that possess the minimum number of spanning trees. We show that the skeleton of each graph with the minimum number of spanning trees in <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ω</mi></mrow></msub></math></span> is either <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></math></span>, where <em>a</em> and <em>b</em> are positive integers with <span><math><mn>2</mn><mo>≤</mo><mi>a</mi><mo>≤</mo><mi>b</mi></math></span> and <span><math><mo>(</mo><mi>a</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>b</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>ω</mi></math></span>, or <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>a</mi><mo>;</mo><mi>b</mi></mrow><mrow><mi>c</mi></mrow></msubsup></math></span>, where <span><math><mi>a</mi><mo>,</mo><mi>b</mi></math></span> and <em>c</em> are positive integers satisfying <span><math><mn>2</mn><mo>≤</mo><mi>c</mi><mo>&lt;</mo><mi>a</mi><mo>≤</mo><mi>b</mi></math></span> and <span><math><mi>c</mi><mo>−</mo><mn>1</mn><mo>+</mo><mo>(</mo><mi>a</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>b</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>=</mo><mi>ω</mi></math></span>. In addition, we establish some structural properties by the method of analysis to further reduce those candidate graphs.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114514"},"PeriodicalIF":0.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759069","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":"Topology and approximation of weak G-bundles in the supercritical dimensions","authors":"Swarnendu Sil","doi":"10.1016/j.aim.2025.110229","DOIUrl":"10.1016/j.aim.2025.110229","url":null,"abstract":"<div><div>For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principal <em>G</em>-bundles are not continuous and thus the usual notion of topology does not make sense. In this work, we develop the notion of a topological isomorphism class for a bundle-connection pair <span><math><mo>(</mo><mi>P</mi><mo>,</mo><mi>A</mi><mo>)</mo></math></span> and use these notions to derive several approximability results for bundles and connections in the Morrey-Sobolev setting. Our proofs follow a connection-oriented approach and also highlight the fact that in the low regularity regime, the regularity of the bundle and connection are intertwined. Our results parallel the theory of the topological degree and approximation results for manifold-valued VMO maps.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110229"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the maximum number of r-cliques in graphs free of complete r-partite subgraphs","authors":"József Balogh ,&nbsp;Suyun Jiang ,&nbsp;Haoran Luo","doi":"10.1016/j.disc.2025.114508","DOIUrl":"10.1016/j.disc.2025.114508","url":null,"abstract":"<div><div>We estimate the maximum possible number of cliques of size <em>r</em> in an <em>n</em>-vertex graph free of a fixed complete <em>r</em>-partite graph <span><math><msub><mrow><mi>K</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow></msub></math></span>. By viewing every <em>r</em>-clique as a hyperedge, the upper bound on the Turán number of the complete <em>r</em>-partite hypergraphs gives the upper bound <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn><mo>/</mo><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mo>)</mo></mrow></math></span>. We improve this to <span><math><mi>o</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn><mo>/</mo><msubsup><mrow><mo>∏</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mo>)</mo></mrow></math></span>. The main tool in our proof is the graph removal lemma. We also provide several lower bound constructions.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114508"},"PeriodicalIF":0.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761179","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":"Representable distributive quasi relation algebras","authors":"Andrew Craig,&nbsp;Claudette Robinson","doi":"10.1007/s00012-025-00884-w","DOIUrl":"10.1007/s00012-025-00884-w","url":null,"abstract":"<div><p>We give a definition of representability for distributive quasi relation algebras (DqRAs). These algebras are a generalisation of relation algebras and were first described by Galatos and Jipsen (Algebra Univers 69:1–21, 2013). Our definition uses a construction that starts with a poset. The algebra is concretely constructed as the lattice of upsets of a partially ordered equivalence relation. The key to defining the three negation-like unary operations is to impose certain symmetry requirements on the partial order. Our definition of representable distributive quasi relation algebras is easily seen to be a generalisation of the definition of representable relations algebras by Jónsson and Tarski (AMS 54:89, 1948). We give examples of representable DqRAs and give a necessary condition for an algebra to be finitely representable. We leave open the questions of whether every DqRA is representable, and also whether the class of representable DqRAs forms a variety. Moreover, our definition provides many other opportunities for investigations in the spirit of those carried out for representable relation algebras.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-025-00884-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The saturation number of C6","authors":"Yongxin Lan ,&nbsp;Yongtang Shi ,&nbsp;Yiqiao Wang ,&nbsp;Junxue Zhang","doi":"10.1016/j.disc.2025.114504","DOIUrl":"10.1016/j.disc.2025.114504","url":null,"abstract":"<div><div>A graph <em>G</em> is called <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-saturated if <em>G</em> is <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-free but <span><math><mi>G</mi><mo>+</mo><mi>e</mi></math></span> is not for any <span><math><mi>e</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mover><mrow><mi>G</mi></mrow><mo>‾</mo></mover><mo>)</mo></math></span>. The saturation number of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>, denoted <span><math><mi>s</mi><mi>a</mi><mi>t</mi><mo>(</mo><mi>n</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span>, is the minimum number of edges in a <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>-saturated graph on <em>n</em> vertices. Finding the exact values of <span><math><mi>s</mi><mi>a</mi><mi>t</mi><mo>(</mo><mi>n</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span> has been one of the most intriguing open problems in extremal graph theory. In this paper, we study the saturation number of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msub></math></span>. We prove that <span><math><mn>4</mn><mi>n</mi><mo>/</mo><mn>3</mn><mo>−</mo><mn>2</mn><mo>≤</mo><mi>s</mi><mi>a</mi><mi>t</mi><mo>(</mo><mi>n</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>)</mo><mo>≤</mo><mo>(</mo><mn>4</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>3</mn></math></span> for all <span><math><mi>n</mi><mo>≥</mo><mn>9</mn></math></span>, which significantly improves the existing lower and upper bounds for <span><math><mi>s</mi><mi>a</mi><mi>t</mi><mo>(</mo><mi>n</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114504"},"PeriodicalIF":0.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761183","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":"Exceptional 2-to-1 rational functions","authors":"Zhiguo Ding ,&nbsp;Michael E. Zieve","doi":"10.1016/j.jcta.2025.106046","DOIUrl":"10.1016/j.jcta.2025.106046","url":null,"abstract":"<div><div>For each odd prime power <em>q</em>, we describe a class of rational functions <span><math><mi>f</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> with the following unusual property: for every odd <em>j</em>, the function induced by <span><math><mi>f</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> on <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>j</mi></mrow></msup></mrow></msub><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> is 2-to-1. We also show that, among all known rational functions <span><math><mi>f</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> which are 2-to-1 on <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>j</mi></mrow></msup></mrow></msub><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span> for infinitely many <em>j</em>, our new functions are the only ones which cannot be written as compositions of rational functions of degree at most four, monomials, Dickson polynomials, and additive (linearized) polynomials.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"215 ","pages":"Article 106046"},"PeriodicalIF":0.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parity statistics on restricted permutations and the Catalan–Schett polynomials","authors":"Zhicong Lin ,&nbsp;Jing Liu ,&nbsp;Sherry H.F. Yan","doi":"10.1016/j.jcta.2025.106049","DOIUrl":"10.1016/j.jcta.2025.106049","url":null,"abstract":"<div><div>Motivated by Kitaev and Zhang's recent work on non-overlapping ascents in stack-sortable permutations and Dumont's permutation interpretation of the Jacobi elliptic functions, we investigate some parity statistics on restricted permutations. Some new related bijections are constructed and two refinements of the generating function for descents over 321-avoiding permutations due to Barnabei, Bonetti and Silimbanian are obtained. In particular, an open problem of Kitaev and Zhang about non-overlapping ascents on 321-avoiding permutations is solved and several combinatorial interpretations for the Catalan–Schett polynomials are found. The stack-sortable permutations are at the heart of our approaches.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"215 ","pages":"Article 106049"},"PeriodicalIF":0.9,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hyperbolic distortion and conformality at the boundary","authors":"Pavel Gumenyuk ,&nbsp;Maria Kourou ,&nbsp;Annika Moucha ,&nbsp;Oliver Roth","doi":"10.1016/j.aim.2025.110251","DOIUrl":"10.1016/j.aim.2025.110251","url":null,"abstract":"<div><div>We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point — the existence of a finite angular derivative in the sense of Carathéodory and the weaker property of angle preservation — in terms of the non-tangential asymptotic behavior of the hyperbolic distortion of the map. We also provide an operator-theoretic characterization of the existence of a finite angular derivative based on Hilbert space methods. As an application we study the backward dynamics of discrete dynamical systems induced by holomorphic self-maps, and characterize the regularity of the associated pre-models in terms of a Blaschke-type condition involving the hyperbolic distortion along regular backward orbits.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"470 ","pages":"Article 110251"},"PeriodicalIF":1.5,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rainbow directed version of Dirac's theorem","authors":"Hao Li ,&nbsp;Luyi Li ,&nbsp;Ping Li ,&nbsp;Xueliang Li","doi":"10.1016/j.disc.2025.114506","DOIUrl":"10.1016/j.disc.2025.114506","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><mi>i</mi><mo>∈</mo><mo>[</mo><mi>s</mi><mo>]</mo><mo>}</mo></math></span> be a collection of not necessarily distinct graphs on the same vertex set <em>V</em>. A graph <em>H</em> is called <em>rainbow</em> in <span><math><mi>G</mi></math></span> if any two edges of <em>H</em> belong to different graphs of <span><math><mi>G</mi></math></span>. In 2020, Joos and Kim proved a rainbow version of Dirac's theorem. In this paper, we prove a rainbow directed version of Dirac's theorem asymptotically: For each <span><math><mn>0</mn><mo>&lt;</mo><mi>ε</mi><mo>&lt;</mo><mn>1</mn></math></span>, there exists an integer <em>N</em> such that when <span><math><mi>n</mi><mo>≥</mo><mi>N</mi></math></span> the following holds. Let <span><math><mi>D</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><mi>i</mi><mo>∈</mo><mo>[</mo><mi>n</mi><mo>]</mo><mo>}</mo></math></span> be a collection of <em>n</em>-vertex digraphs on the same vertex set <em>V</em>. If both the out-degree and the in-degree of <em>v</em> are at least <span><math><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>ε</mi><mo>)</mo></mrow><mi>n</mi></math></span> for each vertex <span><math><mi>v</mi><mo>∈</mo><mi>V</mi></math></span> and each integer <span><math><mi>i</mi><mo>∈</mo><mo>[</mo><mi>n</mi><mo>]</mo></math></span>, then <span><math><mi>D</mi></math></span> contains a rainbow Hamiltonian cycle. Furthermore, we provide a sufficient condition for the existence of arbitrary rainbow tournaments in a collection of <em>n</em>-vertex digraphs, where a <em>tournament</em> is an oriented graph of a complete graph.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114506"},"PeriodicalIF":0.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761335","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}