Graphs and Combinatorics最新文献_第4页

Bounds for DP Color Function and Canonical Labelings DP 颜色函数和规范标签的界限

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-20 DOI: 10.1007/s00373-024-02794-5

Ziqing Li, Yan Yang

{"title":"Bounds for DP Color Function and Canonical Labelings","authors":"Ziqing Li, Yan Yang","doi":"10.1007/s00373-024-02794-5","DOIUrl":"https://doi.org/10.1007/s00373-024-02794-5","url":null,"abstract":"The DP-coloring is a generalization of the list coloring, introduced by Dvořák and Postle. Let ({mathcal {H}}=(L,H)) be a cover of a graph G and (P_{DP}(G,{mathcal {H}})) be the number of ({mathcal {H}})-colorings of G. The DP color function (P_{DP}(G,m)) of G, introduced by Kaul and Mudrock, is the minimum value of (P_{DP}(G,{mathcal {H}})) where the minimum is taken over all possible m-fold covers ({mathcal {H}}) of G. For the family of n-vertex connected graphs, one can deduce that trees maximize the DP color function, from two results of Kaul and Mudrock. In this paper we obtain tight upper bounds for the DP color function of n-vertex 2-connected graphs. Another concern in this paper is the canonical labeling in a cover. It is well known that if an m-fold cover ({mathcal {H}}) of a graph G has a canonical labeling, then (P_{DP}(G,{mathcal {H}})=P(G,m)) in which P(G, m) is the chromatic polynomial of G. However the converse statement of this conclusion is not always true. We give examples that for some m and G, there exists an m-fold cover ({mathcal {H}}) of G such that (P_{DP}(G,{mathcal {H}})=P(G,m)), but ({mathcal {H}}) has no canonical labelings. We also prove that when G is a unicyclic graph or a theta graph, for each (mge 3), if (P_{DP}(G,{mathcal {H}})=P (G,m)), then ({mathcal {H}}) has a canonical labeling.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153770","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

An Alon–Tarsi Style Theorem for Additive Colorings 加色法的阿隆-塔西式定理

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-20 DOI: 10.1007/s00373-024-02797-2

Ian Gossett

引用次数: 0

Critical Subgraphs of Schrijver Graphs for the Fractional Chromatic Number 分数色度数的 Schrijver 图临界子图

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-10 DOI: 10.1007/s00373-024-02782-9

Anna Gujgiczer, Gábor Simonyi

引用次数: 0

Weak External Bisections of Regular Graphs 正则图的弱外部平分线

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-07 DOI: 10.1007/s00373-024-02796-3

Juan Yan, Ya-Hong Chen

引用次数: 0

Almost Intersecting Families for Vector Spaces 向量空间的几乎相交族

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-07 DOI: 10.1007/s00373-024-02790-9

Yunjing Shan, Junling Zhou

{"title":"Almost Intersecting Families for Vector Spaces","authors":"Yunjing Shan, Junling Zhou","doi":"10.1007/s00373-024-02790-9","DOIUrl":"https://doi.org/10.1007/s00373-024-02790-9","url":null,"abstract":"Let V be an n-dimensional vector space over the finite field ({mathbb {F}}_{q}) and let (left[ begin{array}{c} V k end{array}right] _q) denote the family of all k-dimensional subspaces of V. A family ({{mathcal {F}}}subseteq left[ begin{array}{c} V k end{array}right] _q) is called intersecting if for all F, (F'in {{mathcal {F}}},) we have ({textrm{dim}}(Fcap F')ge 1.) A family ({{mathcal {F}}}subseteq left[ begin{array}{c} V k end{array}right] _q) is called almost intersecting if for every (Fin {{mathcal {F}}}) there is at most one element (F'in {{mathcal {F}}}) satisfying ({textrm{dim}}(Fcap F')=0.) In this paper we investigate almost intersecting families in the vector space V. Firstly, for large n, we determine the maximum size of an almost intersecting family in (left[ begin{array}{c} V k end{array}right] _q,) which is the same as that of an intersecting family. Secondly, we characterize the structures of all maximum almost intersecting families under the condition that they are not intersecting.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889719","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

Closed-Form Solution of Conic in Point-Line Enumerative Problem of Conic 圆锥曲线点-线枚举问题的闭式解法

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-06 DOI: 10.1007/s00373-024-02793-6

Yang Guo

引用次数: 0

Parameters of Quotient-Polynomial Graphs 二次多项式图的参数

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-05 DOI: 10.1007/s00373-024-02789-2

Allen Herman, Roghayeh Maleki

引用次数: 0

Ternary Extremal Four-Negacirculant Self-Dual Codes 三元极值四反循环自偶码

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-05-02 DOI: 10.1007/s00373-024-02788-3

Masaaki Harada, Keita Ishizuka, Hadi Kharaghani

引用次数: 0

Reduced Clique Graphs: A Correction to “Chordal Graphs and Their Clique Graphs” 还原簇图：对 "弦图及其簇图 "的更正

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-24 DOI: 10.1007/s00373-024-02786-5

Dillon Mayhew, Andrew Probert

{"title":"Reduced Clique Graphs: A Correction to “Chordal Graphs and Their Clique Graphs”","authors":"Dillon Mayhew, Andrew Probert","doi":"10.1007/s00373-024-02786-5","DOIUrl":"https://doi.org/10.1007/s00373-024-02786-5","url":null,"abstract":"Galinier, Habib, and Paul introduced the reduced clique graph of a chordal graph G. The nodes of the reduced clique graph are the maximal cliques of G, and two nodes are joined by an edge if and only if they form a non-disjoint separating pair of cliques in G. In this case the weight of the edge is the size of the intersection of the two cliques. A clique tree of G is a tree with the maximal cliques of G as its nodes, where for any (vin V(G)), the subgraph induced by the nodes containing v is connected. Galinier et al. prove that a spanning tree of the reduced clique graph is a clique tree if and only if it has maximum weight, but their proof contains an error. We explain and correct this error. In addition, we initiate a study of the structure of reduced clique graphs by proving that they cannot contain any induced cycle of length five (although they may contain induced cycles of length three or any even integer greater than two). We show that no cycle of length four or more is isomorphic to a reduced clique graph. We prove that the class of clique graphs of chordal graphs is not comparable to the class of reduced clique graphs of chordal graphs by providing examples that are in each of these classes without being in the other.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800759","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

Extremal Graph Theoretic Questions for q-Ary Vectors q-Ary 向量的极值图论问题

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-04-24 DOI: 10.1007/s00373-024-02787-4

Balázs Patkós, Zsolt Tuza, Máté Vizer

{"title":"Extremal Graph Theoretic Questions for q-Ary Vectors","authors":"Balázs Patkós, Zsolt Tuza, Máté Vizer","doi":"10.1007/s00373-024-02787-4","DOIUrl":"https://doi.org/10.1007/s00373-024-02787-4","url":null,"abstract":"A q-graph H on n vertices is a set of vectors of length n with all entries from ({0,1,dots ,q}) and every vector (that we call a q-edge) having exactly two non-zero entries. The support of a q-edge ({textbf{x}}) is the pair (S_{textbf{x}}) of indices of non-zero entries. We say that H is an s-copy of an ordinary graph F if (|H|=|E(F)|), F is isomorphic to the graph with edge set ({S_{textbf{x}}:{textbf{x}}in H}), and whenever (vin e,e'in E(F)), the entries with index corresponding to v in the q-edges corresponding to e and (e') sum up to at least s. E.g., the q-edges (1, 3, 0, 0, 0), (0, 1, 0, 0, 3), and (3, 0, 0, 0, 1) form a 4-triangle. The Turán number (mathop {}!textrm{ex}(n,F,q,s)) is the maximum number of q-edges that a q-graph H on n vertices can have if it does not contain any s-copies of F. In the present paper, we determine the asymptotics of (mathop {}!textrm{ex}(n,F,q,q+1)) for many graphs F.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"50 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800763","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