Electronic Journal of Combinatorics最新文献_第3页

Improved Pyrotechnics: Closer to the Burning Number Conjecture 改进的烟火:更接近燃烧数猜想

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-10-06 DOI: 10.37236/11113

Paul Bastide, Marthe Bonamy, Anthony Bonato, Pierre Charbit, Shahin Kamali, Théo Pierron, Mikaël Rabie

引用次数: 0

Lower Bounds for the Turán Densities of Daisies 雏菊Turán密度的下界

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-10-06 DOI: 10.37236/11206

David Ellis, Dylan King

引用次数: 1

Cut Vertices in Random Planar Maps 在随机平面图中切割顶点

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/11163

Michael Drmota, Marc Noy, Benedikt Stufler

引用次数: 0

An Aα-Spectral Erdős-Sós Theorem a α-谱Erdős-Sós定理

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/11593

Ming-Zhu Chen, Shuchao Li, Zhao-Ming Li, Yuantian Yu, Xiao-Dong Zhang

{"title":"An Aα-Spectral Erdős-Sós Theorem","authors":"Ming-Zhu Chen, Shuchao Li, Zhao-Ming Li, Yuantian Yu, Xiao-Dong Zhang","doi":"10.37236/11593","DOIUrl":"https://doi.org/10.37236/11593","url":null,"abstract":"Let $G$ be a graph and let $alpha$ be a real number in $[0,1].$ In 2017, Nikiforov proposed the $A_alpha$-matrix for $G$ as $A_{alpha}(G)=alpha D(G)+(1-alpha)A(G)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the degree diagonal matrix of $G$, respectively. The largest eigenvalue of $A_{alpha}(G)$ is called the $A_alpha$-index of $G.$ The famous Erdős-Sós conjecture states that every $n$-vertex graph with more than $frac{1}{2}(k-1)n$ edges must contain every tree on $k+1$ vertices. In this paper, we consider an $A_alpha$-spectral version of this conjecture. For $n>k,$ let $S_{n,k}$ be the join of a clique on $k$ vertices with an independent set of $n-k$ vertices and denote by $S^+_{n,k}$ the graph obtained from $S_{n,k}$ by adding one edge. We show that for fixed $kgeq2,,0<alpha<1$ and $ngeqfrac{88k^2(k+1)^2}{alpha^4(1-alpha)}$, if a graph on $n$ vertices has $A_alpha$-index at least as large as $S_{n,k}$ (resp. $S^+_{n,k}$), then it contains all trees on $2k+2$ (resp. $2k+3$) vertices, or it is isomorphic to $S_{n,k}$ (resp. $S^+_{n,k}$). These extend the results of Cioabă, Desai and Tait (2022), in which they confirmed the adjacency spectral version of the Erdős-Sós conjecture.","PeriodicalId":11515,"journal":{"name":"Electronic Journal of Combinatorics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136011694","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

Proving a Directed Analogue of the Gyárfás-Sumner Conjecture for Orientations of $P_4$ 证明$P_4$取向的Gyárfás-Sumner猜想的一个有向模拟

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/11538

Linda Cook, Tomáš Masařík, Marcin Pilipczuk, Amadeus Reinald, Uéverton S. Souza

{"title":"Proving a Directed Analogue of the Gyárfás-Sumner Conjecture for Orientations of $P_4$","authors":"Linda Cook, Tomáš Masařík, Marcin Pilipczuk, Amadeus Reinald, Uéverton S. Souza","doi":"10.37236/11538","DOIUrl":"https://doi.org/10.37236/11538","url":null,"abstract":"An oriented graph is a digraph that does not contain a directed cycle of length two. An (oriented) graph $D$ is $H$-free if $D$ does not contain $H$ as an induced sub(di)graph. The Gyárfás-Sumner conjecture is a widely-open conjecture on simple graphs, which states that for any forest $F$, there is some function $f$ such that every $F$-free graph $G$ with clique number $omega(D)$ has chromatic number at most $f(omega(D))$. Aboulker, Charbit, and Naserasr [Extension of Gyárfás-Sumner Conjecture to Digraphs, Electron. J. Comb., 2021] proposed an analogue of this conjecture to the dichromatic number of oriented graphs. The dichromatic number of a digraph $D$ is the minimum number of colors required to color the vertex set of $D$ so that no directed cycle in $D$ is monochromatic. Aboulker, Charbit, and Naserasr’s $overrightarrow{chi}$ -boundedness conjecture states that for every oriented forest $F$, there is some function f such that every $F$-free oriented graph $D$ has dichromatic number at most $f(omega(D))$, where $omega(D)$ is the size of a maximum clique in the graph underlying $D$. In this paper, we perform the first step towards proving Aboulker, Charbit, and Naserasr’s $overrightarrow{chi}$-boundedness conjecture by showing that it holds when $F$ is any orientation of a path on four vertices.","PeriodicalId":11515,"journal":{"name":"Electronic Journal of Combinatorics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136011693","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

Bounding Generalized Coloring Numbers of Planar Graphs Using Coin Models 利用硬币模型的平面图的边界广义着色数

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/11095

Jesper Nederlof, Michał Pilipczuk, Karol Węgrzycki

引用次数: 1

Extended Double Covers and Homomorphism Bounds of Signed Graphs 符号图的扩展双盖与同态界

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/10754

Florent Foucaud, Reza Naserasr, Rongxing Xu

{"title":"Extended Double Covers and Homomorphism Bounds of Signed Graphs","authors":"Florent Foucaud, Reza Naserasr, Rongxing Xu","doi":"10.37236/10754","DOIUrl":"https://doi.org/10.37236/10754","url":null,"abstract":"A signed graph $(G, sigma)$ is a graph $G$ together with an assignment $sigma:E(G) rightarrow {+,-}$. The notion of homomorphisms of signed graphs is a relatively new development which allows to strengthen the connection between the theories of minors and colorings of graphs. Following this thread of thoughts, we investigate this connection through the notion of Extended Double Covers of signed graphs, which was recently introduced by Naserasr, Sopena and Zaslavsky. More precisely, we say that a signed graph $(B, pi)$ is planar-complete if any signed planar graph $(G, sigma)$ which verifies the conditions of a basic no-homomorphism lemma with respect to $(B,pi)$ admits a homomorphism to $(B, pi)$. Our conjecture then is that: if $(B, pi)$ is a connected signed graph with no positive odd closed walk which is planar-complete, then its Extended Double Cover ${rm EDC}(B,pi)$ is also planar-complete. We observe that this conjecture largely extends the Four-Color Theorem and is strongly connected to a number of conjectures in extension of this famous theorem. A given (signed) graph $(B,pi)$ bounds a class of (signed) graphs if every (signed) graph in the class admits a homomorphism to $(B,pi)$.In this work, and in support of our conjecture, we prove it for the subclass of signed $K_4$-minor free graphs. Inspired by this development, we then investigate the problem of finding optimal homomorphism bounds for subclasses of signed $K_4$-minor-free graphs with restrictions on their girth and we present nearly optimal solutions. Our work furthermore leads to the development of weighted signed graphs.","PeriodicalId":11515,"journal":{"name":"Electronic Journal of Combinatorics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136010813","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

Quantum Continuants, Quantum Rotundus and Triangulations of Annuli 量子连续面、量子旋转面和环面的三角剖分

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-22 DOI: 10.37236/11400

Ludivine Leclere, Sophie Morier-Genoud

引用次数: 0

Irreducible Subcube Partitions 不可约子立方体分区

4区数学

Electronic Journal of Combinatorics Pub Date : 2023-09-08 DOI: 10.37236/11862

Yuval Filmus, Edward A. Hirsch, Sascha Kurz, Ferdinand Ihringer, Artur Ryazanov, Alexander V. Smal, Marc Vinyals

引用次数: 1

Distribution of External Branch Lengths in Yule Histories 圣诞历史中外枝长度的分布