Graphs and Combinatorics最新文献_第2页

On the Sequence with Fewer Subsequence Sums in Finite Abelian Groups 论有限阿贝尔群中具有较少后继和的序列

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-31 DOI: 10.1007/s00373-024-02818-0

Jiangtao Peng, Yue Sun

引用次数: 0

Gallai-Ramsey Multiplicity for Rainbow Small Trees 彩虹小树的加莱-拉姆齐多重性

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-31 DOI: 10.1007/s00373-024-02819-z

Xueliang Li, Yuan Si

引用次数: 0

The Robust Chromatic Number of Graphs 图形的稳健色度数

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-27 DOI: 10.1007/s00373-024-02817-1

Gábor Bacsó, Balázs Patkós, Zsolt Tuza, Máté Vizer

引用次数: 0

Using a Grassmann Graph to Recover the Underlying Projective Geometry 利用格拉斯曼图恢复基本投影几何

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-26 DOI: 10.1007/s00373-024-02816-2

Ian Seong

{"title":"Using a Grassmann Graph to Recover the Underlying Projective Geometry","authors":"Ian Seong","doi":"10.1007/s00373-024-02816-2","DOIUrl":"https://doi.org/10.1007/s00373-024-02816-2","url":null,"abstract":"Let n, k denote integers with (n>2kge 6). Let ({mathbb {F}}_q) denote a finite field with q elements, and let V denote a vector space over ({mathbb {F}}_q) that has dimension n. The projective geometry (P_q(n)) is the partially ordered set consisting of the subspaces of V; the partial order is given by inclusion. For the Grassmann graph (J_q(n,k)) the vertex set consists of the k-dimensional subspaces of V. Two vertices of (J_q(n,k)) are adjacent whenever their intersection has dimension (k-1). The graph (J_q(n,k)) is known to be distance-regular. Let (partial ) denote the path-length distance function of (J_q(n,k)). Pick two vertices x, y in (J_q(n,k)) such that (1<partial (x,y)<k). The set (P_q(n)) contains the elements (x,y,xcap y,x+y). In our main result, we describe (xcap y) and (x+y) using only the graph structure of (J_q(n,k)). To achieve this result, we make heavy use of the Euclidean representation of (J_q(n,k)) that corresponds to the second largest eigenvalue of the adjacency matrix.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770178","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

Covering Array on the Cartesian Product of Hypergraphs 超图笛卡儿积上的覆盖阵列

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-10 DOI: 10.1007/s00373-024-02813-5

Yasmeen Akhtar, Soumen Maity

{"title":"Covering Array on the Cartesian Product of Hypergraphs","authors":"Yasmeen Akhtar, Soumen Maity","doi":"10.1007/s00373-024-02813-5","DOIUrl":"https://doi.org/10.1007/s00373-024-02813-5","url":null,"abstract":"Covering array (CA) on a hypergraph H is a combinatorial object used in interaction testing of a complex system modeled as H. Given a t-uniform hypergraph H and positive integer s, it is an array with a column for each vertex having entries from a finite set of cardinality s, such as (mathbb {Z}_s), and the property that any set of t columns that correspond to vertices in a hyperedge covers all (s^t) ordered t-tuples from (mathbb {Z}_s^t) at least once as a row. Minimizing the number of rows (size) of CA is important in industrial applications. Given a hypergraph H, a CA on H with the minimum size is called optimal. Determining the minimum size of CA on a hypergraph is NP-hard. We focus on constructions that make optimal covering arrays on large hypergraphs from smaller ones and discuss the construction method for optimal CA on the Cartesian product of a Cayley hypergraph with different families of hypergraphs. For a prime power (q>2), we present a polynomial-time approximation algorithm with approximation ratio (left( Big lceil log _qleft( frac{|V|}{3^{k-1}}right) Big rceil right) ^2) for constructing covering array CA(n, H, q) on 3-uniform hypergraph (H=(V,E)) with (k>1) prime factors with respect to the Cartesian product.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141569422","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

Graphs G Where $$G-N[v]$$ is a Tree for Each Vertex v 其中 $$G-N[v]$$ 是每个顶点 v 的树的图形 G

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-06 DOI: 10.1007/s00373-024-02814-4

Bo Zhang, Baoyindureng Wu

{"title":"Graphs G Where $$G-N[v]$$ is a Tree for Each Vertex v","authors":"Bo Zhang, Baoyindureng Wu","doi":"10.1007/s00373-024-02814-4","DOIUrl":"https://doi.org/10.1007/s00373-024-02814-4","url":null,"abstract":"A given graph H is called realizable by a graph G if (G[N(v)]cong H) for every vertex v of G. The Trahtenbrot-Zykov problem says that which graphs are realizable? We consider a problem somewhat opposite in a more general setting. Let ({mathcal {F}}) be a family of graphs: to characterize all graphs G such that (G-N[v]in {mathcal {F}}) for every vertex v of G. Let ({mathcal {T}}_m) be the set of all trees of size (mge 0) for a fixed nonnegative integer m, ({mathcal {P}}={P_t: t>0}) and ({mathcal {S}}={K_{1,t}: tge 0}). We show that for a connected graph G with its complement ({overline{G}}) being connected, (G-N[v]in {mathcal {T}}_m) for each (vin V(G)) if and only if one of the following holds: (G-N[v]cong K_{1,m}) for each (vin V(G)), or (G-N[v]cong P_{m+1}) for each (vin V(G)). Indeed, the graphs with later two properties are characterized by the same authors very recently (Graphs G in which (G-N[v]) has a prescribed property for each vertex v, Discrete Appl. Math., In press.). In addition, we characterize all graphs G such that (G-N[v]in {mathcal {S}}) for each (vin V(G)) and all graphs G such that (G-N[v]in {mathcal {P}}) for each (vin V(G)). This solves an open problem raised by Yu and Wu (Graphs in which (G-N[v]) is a cycle for each vertex v, Discrete Math. 344 (2021) 112519). Finally, a number of conjectures are proposed for the perspective of the problem.","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577387","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

Some Two-Weight Codes Over Chain Rings and their Strongly Regular Graphs 链环上的一些二重编码及其强正则图

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-07-05 DOI: 10.1007/s00373-024-02806-4

Minjia Shi, Ruowen Liu, Patrick Solé

引用次数: 0

The Burning Number Conjecture is True for Trees without Degree-2 Vertices 燃烧数猜想适用于没有度数为 2 的顶点的树

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-06-25 DOI: 10.1007/s00373-024-02812-6

Yukihiro Murakami

引用次数: 0

Graphs with Many Independent Vertex Cuts 具有多个独立顶点切分的图形

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-06-25 DOI: 10.1007/s00373-024-02811-7

Yanan Hu, Xingzhi Zhan, Leilei Zhang

引用次数: 0

The Eulerian Distribution on the Fixed-Point Free Involutions of the Hyperoctahedral Group Under the Natural Order 自然秩序下超八面体群定点自由旋转的欧拉分布

IF 0.7 4区数学

Graphs and Combinatorics Pub Date : 2024-06-25 DOI: 10.1007/s00373-024-02805-5

Lingli Wan, Xiaoqin Gao, Frank Z. K. Li, Jane Y. X. Yang

引用次数: 0