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Discussiones Mathematicae Graph Theory最新文献

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High-ordered spectral characterization of unicyclic graphs 单环图的高阶谱表征
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-28 DOI: 10.7151/dmgt.2489
Yi-Zheng Fan, Hong Yang, Jian Zheng
{"title":"High-ordered spectral characterization of unicyclic graphs","authors":"Yi-Zheng Fan, Hong Yang, Jian Zheng","doi":"10.7151/dmgt.2489","DOIUrl":"https://doi.org/10.7151/dmgt.2489","url":null,"abstract":"In this paper we will apply the tensor and its traces to investigate the spectral characterization of unicyclic graphs. Let $G$ be a graph and $G^m$ be the $m$-th power (hypergraph) of $G$. The spectrum of $G$ is referring to its adjacency matrix, and the spectrum of $G^m$ is referring to its adjacency tensor. The graph $G$ is called determined by high-ordered spectra (DHS for short) if, whenever $H$ is a graph such that $H^m$ is cospectral with $G^m$ for all $m$, then $H$ is isomorphic to $G$. In this paper we first give formulas for the traces of the power of unicyclic graphs, and then provide some high-ordered cospectral invariants of unicyclic graphs. We prove that a class of unicyclic graphs with cospectral mates is DHS, and give two examples of infinitely many pairs of cospectral unicyclic graphs but with different high-ordered spectra.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46551000","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}
引用次数: 4
Edge Precoloring Extension of Trees II 树的边缘预着色扩展Ⅱ
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-23 DOI: 10.7151/dmgt.2461
C. J. Casselgren, F. B. Petros
{"title":"Edge Precoloring Extension of Trees II","authors":"C. J. Casselgren, F. B. Petros","doi":"10.7151/dmgt.2461","DOIUrl":"https://doi.org/10.7151/dmgt.2461","url":null,"abstract":"Abstract We consider the problem of extending and avoiding partial edge colorings of trees; that is, given a partial edge coloring φ of a tree T we are interested in whether there is a proper Δ(T )-edge coloring of T that agrees with the coloring φ on every edge that is colored under φ; or, similarly, if there is a proper Δ(T )-edge coloring that disagrees with φ on every edge that is colored under φ. We characterize which partial edge colorings with at most Δ(T ) + 1 precolored edges in a tree T are extendable, thereby proving an analogue of a result by Andersen for Latin squares. Furthermore we obtain some “mixed” results on extending a partial edge coloring subject to the condition that the extension should avoid a given partial edge coloring; in particular, for all 0 ≤ k ≤ Δ(T ), we characterize for which configurations consisting of a partial coloring φ of Δ(T ) − k edges and a partial coloring ψ of k + 1 edges of a tree T, there is an extension of φ that avoids ψ.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46389041","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}
引用次数: 3
Strong Incidence Colouring of Graphs 图的强关联着色
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-23 DOI: 10.7151/dmgt.2466
Brahim Benmedjdoub, É. Sopena
{"title":"Strong Incidence Colouring of Graphs","authors":"Brahim Benmedjdoub, É. Sopena","doi":"10.7151/dmgt.2466","DOIUrl":"https://doi.org/10.7151/dmgt.2466","url":null,"abstract":"Abstract An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f) of G are adjacent whenever (i) v = w, or (ii) e = f, or (iii) vw = e or f. An incidence p-colouring of G is a mapping from the set of incidences of G to the set of colours {1, . . ., p} such that every two adjacent incidences receive distinct colours. Incidence colouring has been introduced by Brualdi and Quinn Massey in 1993 and, since then, studied by several authors. In this paper, we introduce and study the strong version of incidence colouring, where incidences adjacent to the same incidence must also get distinct colours. We determine the exact value of — or upper bounds on — the strong incidence chromatic number of several classes of graphs, namely cycles, wheel graphs, trees, ladder graphs, square grids and subclasses of Halin graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41925627","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}
引用次数: 1
A Note on Minimum Degree, Bipartite Holes, and Hamiltonian Properties 关于最小度、二分空穴和哈密顿性质的一个注记
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-23 DOI: 10.7151/dmgt.2464
Qiannan Zhou, H. Broersma, Ligong Wang, Yong Lu
{"title":"A Note on Minimum Degree, Bipartite Holes, and Hamiltonian Properties","authors":"Qiannan Zhou, H. Broersma, Ligong Wang, Yong Lu","doi":"10.7151/dmgt.2464","DOIUrl":"https://doi.org/10.7151/dmgt.2464","url":null,"abstract":"Abstract We adopt the recently introduced concept of the bipartite-hole-number due to McDiarmid and Yolov, and extend their result on Hamiltonicity to other Hamiltonian properties of graphs with a large minimum degree in terms of this concept. An (s, t)-bipartite-hole in a graph G consists of two disjoint sets of vertices S and T with |S| = s and |T| = t such that E(S, T ) =∅. The bipartite-hole-number α˜(G) tilde alpha left( G right) is the maximum integer r such that G contains an (s, t)-bipartite-hole for every pair of nonnegative integers s and t with s + t = r. Our main results are that a graph G is traceable if δ(G)≥α˜(G)−1 delta left( G right) ge tilde alpha left( G right) - 1 , and Hamilton-connected if δ(G)≥α˜(G)+1 delta left( G right) ge tilde alpha left( G right) + 1 , both improving the analogues of Dirac’s Theorem for traceable and Hamilton-connected graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49619218","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}
引用次数: 0
Outer Connected Domination in Maximal Outerplanar Graphs and Beyond 极大外平面图及其以外的外连通支配
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-23 DOI: 10.7151/dmgt.2462
Wei Yang, Baoyindureng Wu
{"title":"Outer Connected Domination in Maximal Outerplanar Graphs and Beyond","authors":"Wei Yang, Baoyindureng Wu","doi":"10.7151/dmgt.2462","DOIUrl":"https://doi.org/10.7151/dmgt.2462","url":null,"abstract":"Abstract A set S of vertices in a graph G is an outer connected dominating set of G if every vertex in V S is adjacent to a vertex in S and the subgraph induced by V S is connected. The outer connected domination number of G, denoted by γ˜c(G) {tilde gamma _c}left( G right) , is the minimum cardinality of an outer connected dominating set of G. Zhuang [Domination and outer connected domination in maximal outerplanar graphs, Graphs Combin. 37 (2021) 2679–2696] recently proved that γ˜c(G)≤⌊ n+k4 ⌋ {tilde gamma _c}left( G right) le leftlfloor {{{n + k} over 4}} rightrfloor for any maximal outerplanar graph G of order n ≥ 3 with k vertices of degree 2 and posed a conjecture which states that G is a striped maximal outerplanar graph with γ˜c(G)≤⌊ n+24 ⌋ {tilde gamma _c}left( G right) le leftlfloor {{{n + 2} over 4}} rightrfloor if and only if G ∈ 𝒜, where 𝒜 consists of six special families of striped outerplanar graphs. We disprove the conjecture. Moreover, we show that the conjecture become valid under some additional property to the striped maximal outerplanar graphs. In addition, we extend the above theorem of Zhuang to all maximal K2,3-minor free graphs without K4 and all K4-minor free graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45622443","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}
引用次数: 0
Bounds on the Global Double Roman Domination Number in Graphs 图中全局双罗马统治数的界
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-08-23 DOI: 10.7151/dmgt.2460
Guoliang Hao, Shouliu Wei, S. M. Sheikholeslami, Xiaodan Chen
{"title":"Bounds on the Global Double Roman Domination Number in Graphs","authors":"Guoliang Hao, Shouliu Wei, S. M. Sheikholeslami, Xiaodan Chen","doi":"10.7151/dmgt.2460","DOIUrl":"https://doi.org/10.7151/dmgt.2460","url":null,"abstract":"Abstract Let G be a simple graph of order n and let γgdR(G) be the global double Roman domination number of G. In this paper, we give some upper bounds on the global double Roman domination number of G. In particular, we completely characterize the graph G with γgdR(G) = 2n − 2 and γgdR(G) = 2n − 3. Our results answer a question posed by Shao et al. (2019).","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44254559","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}
引用次数: 0
On weakly Turán-good graphs 关于弱Turán-good图
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-07-25 DOI: 10.7151/dmgt.2510
Dániel Gerbner
{"title":"On weakly Turán-good graphs","authors":"Dániel Gerbner","doi":"10.7151/dmgt.2510","DOIUrl":"https://doi.org/10.7151/dmgt.2510","url":null,"abstract":"Given graphs $H$ and $F$ with $chi(H)<chi(F)$, we say that $H$ is weakly $F$-Tur'an-good if among $n$-vertex $F$-free graphs, a $(chi(F)-1)$-partite graph contains the most copies of $H$. Let $H$ be a bipartite graph that contains a complete bipartite subgraph $K$ such that each vertex of $H$ is adjacent to a vertex of $K$. We show that $H$ is weakly $K_3$-Tur'an-good, improving a very recent asymptotic bound due to Grzesik, GyH ori, Salia and Tompkins. They also showed that for any $r$ there exist graphs that are not weakly $K_r$-Tur'an-good. We show that for any non-bipartite $F$ there exists graphs that are not weakly $F$-Tur'an-good. We also show examples of graphs that are $C_{2k+1}$-Tur'an-good but not $C_{2ell+1}$-Tur'an-good for every $k>ell$.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48890941","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}
引用次数: 2
Covering the Edges of a Random Hypergraph by Cliques 用团覆盖随机超图的边
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2431
V. Rödl, A. Rucinski
{"title":"Covering the Edges of a Random Hypergraph by Cliques","authors":"V. Rödl, A. Rucinski","doi":"10.7151/dmgt.2431","DOIUrl":"https://doi.org/10.7151/dmgt.2431","url":null,"abstract":"Abstract We determine the order of magnitude of the minimum clique cover of the edges of a binomial, r-uniform, random hypergraph G(r)(n, p), p fixed. In doing so, we combine the ideas from the proofs of the graph case (r = 2) in Frieze and Reed [Covering the edges of a random graph by cliques, Combinatorica 15 (1995) 489–497] and Guo, Patten, Warnke [Prague dimension of random graphs, manuscript submitted for publication].","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49227128","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}
引用次数: 0
(C3, C4, C5, C7)-Free Almost Well-Dominated Graphs （C3，C4，C5，C7）-自由几乎良控制图
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2331
Hadi Alizadeh, Didem Gözüpek, Gülnaz Boruzanli Ekinci
{"title":"(C3, C4, C5, C7)-Free Almost Well-Dominated Graphs","authors":"Hadi Alizadeh, Didem Gözüpek, Gülnaz Boruzanli Ekinci","doi":"10.7151/dmgt.2331","DOIUrl":"https://doi.org/10.7151/dmgt.2331","url":null,"abstract":"Abstract The domination gap of a graph G is defined as the di erence between the maximum and minimum cardinalities of a minimal dominating set in G. The term well-dominated graphs referring to the graphs with domination gap zero, was first introduced by Finbow et al. [Well-dominated graphs: A collection of well-covered ones, Ars Combin. 25 (1988) 5–10]. In this paper, we focus on the graphs with domination gap one which we term almost well-dominated graphs. While the results by Finbow et al. have implications for almost well-dominated graphs with girth at least 8, we extend these results to (C3, C4, C5, C7)-free almost well-dominated graphs by giving a complete structural characterization for such graphs.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47958867","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}
引用次数: 0
Decomposing 10-Regular Graphs into Paths of Length 5 将10个正则图分解为长度为5的路径
IF 0.7 4区 数学
Discussiones Mathematicae Graph Theory Pub Date : 2022-07-12 DOI: 10.7151/dmgt.2334
Mengmeng Xie, Chuixiang Zhou
{"title":"Decomposing 10-Regular Graphs into Paths of Length 5","authors":"Mengmeng Xie, Chuixiang Zhou","doi":"10.7151/dmgt.2334","DOIUrl":"https://doi.org/10.7151/dmgt.2334","url":null,"abstract":"Abstract Let G be a 10-regular graph which does not contain any 4-cycles. In this paper, we prove that G can be decomposed into paths of length 5, such that every vertex is a terminal of exactly two paths.","PeriodicalId":48875,"journal":{"name":"Discussiones Mathematicae Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45589257","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}
引用次数: 1
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