Discrete Mathematics最新文献_第8页

On Steinerberger curvature and graph distance matrices 关于steinberger曲率和图距离矩阵

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-07 DOI: 10.1016/j.disc.2025.114475

Wei-Chia Chen , Mao-Pei Tsui

引用次数: 0

Proof of a conjecture on connectivity keeping odd paths in k-connected bipartite graphs k连通二部图中保持奇路径的连通性猜想的证明

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-07 DOI: 10.1016/j.disc.2025.114476

Qing Yang, Yingzhi Tian

{"title":"Proof of a conjecture on connectivity keeping odd paths in k-connected bipartite graphs","authors":"Qing Yang, Yingzhi Tian","doi":"10.1016/j.disc.2025.114476","DOIUrl":"10.1016/j.disc.2025.114476","url":null,"abstract":"<div><div>Luo, Tian and Wu (2022) conjectured that for any tree T with bipartition X and Y, every k-connected bipartite graph G with minimum degree at least <math><mi>k</mi><mo>+</mo><mi>t</mi></math>, where <math><mi>t</mi><mo>=</mo><mi>max</mi><mo>⁡</mo><mo>{</mo><mo>|</mo><mi>X</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>}</mo></math>, contains a tree <math><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>≅</mo><mi>T</mi></math> such that <math><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></math> is still k-connected. Note that <math><mi>t</mi><mo>=</mo><mo>⌈</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math> when the tree T is the path with order m. In this paper, we prove that every k-connected bipartite graph G with minimum degree at least <math><mi>k</mi><mo>+</mo><mo>⌈</mo><mfrac><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math> contains a path P of order m such that <math><mi>G</mi><mo>−</mo><mi>V</mi><mo>(</mo><mi>P</mi><mo>)</mo></math> remains k-connected. This shows that the conjecture is true for paths with odd order. For paths with even order, the minimum degree bound in this paper is the bound in the conjecture plus one.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 8","pages":"Article 114476"},"PeriodicalIF":0.7,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563866","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}

引用次数: 0

Induced saturation for complete bipartite posets 完全二部偏集的诱导饱和

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-05 DOI: 10.1016/j.disc.2025.114462

Dingyuan Liu

引用次数: 0

The Ramsey numbers for certain large trees of order n with maximum degree at most n − 6 versus the wheel of order nine 最大度不超过n的n阶大树 − 6与9阶轮盘的Ramsey数

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-04 DOI: 10.1016/j.disc.2025.114461

Thomas Britz , Zhi Yee Chng , Kok Bin Wong

引用次数: 0

A large minimal blocker for 123-avoiding permutations 一个大的最小阻挡123避免排列

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-04 DOI: 10.1016/j.disc.2025.114463

Yaroslav Shitov

引用次数: 0

Several classes of minimal linear codes from vectorial Boolean functions and p-ary functions 向量布尔函数和p元函数的几种最小线性码

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-04 DOI: 10.1016/j.disc.2025.114464

Wengang Jin, Kangquan Li, Longjiang Qu

{"title":"Several classes of minimal linear codes from vectorial Boolean functions and p-ary functions","authors":"Wengang Jin, Kangquan Li, Longjiang Qu","doi":"10.1016/j.disc.2025.114464","DOIUrl":"10.1016/j.disc.2025.114464","url":null,"abstract":"<div><div>Minimal linear codes are widely used in secret sharing schemes and secure two-party computation. Most of the minimal linear codes constructed satisfy the Ashikhmin-Barg (AB for short) condition. However, up to now, only a small classes of minimal linear codes violating the AB condition have been presented in the literature. In this paper, we are devoted to constructing more classes of minimal linear codes over the finite field <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math> that violate the AB condition and have new parameters. First, we provide several classes of minimal linear codes violating the AB condition from vectorial Boolean functions and determine their weight distributions. Then, we obtain new p-ary functions over the finite fields <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math> with p an odd prime and determine their Walsh spectrum distributions. Finally, the resulted p-ary functions are employed to construct several classes of linear codes with two to four weights. In these codes, one class is minimal and violates the AB condition, and two classes satisfy the AB condition.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114464"},"PeriodicalIF":0.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535041","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}

引用次数: 0

Induced matching vs edge open packing: Trees and product graphs 诱导匹配与边缘开放填充：树和积图

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-04 DOI: 10.1016/j.disc.2025.114458

Boštjan Brešar , Tanja Dravec , Jaka Hedžet , Babak Samadi

{"title":"Induced matching vs edge open packing: Trees and product graphs","authors":"Boštjan Brešar , Tanja Dravec , Jaka Hedžet , Babak Samadi","doi":"10.1016/j.disc.2025.114458","DOIUrl":"10.1016/j.disc.2025.114458","url":null,"abstract":"<div><div>Given a graph G, the maximum size of an induced subgraph of G each component of which is a star is called the edge open packing number, <math><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>e</mi></mrow><mrow><mi>o</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math>, of G. Similarly, the maximum size of an induced subgraph of G each component of which is the star <math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math> is the induced matching number, <math><msub><mrow><mi>ν</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math>, of G. While the inequality <math><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>e</mi></mrow><mrow><mi>o</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math> clearly holds for all graphs G, we provide a structural characterization of those trees that attain the equality. We prove that the induced matching number of the lexicographic product <math><mi>G</mi><mo>∘</mo><mi>H</mi></math> of arbitrary two graphs G and H equals <math><mi>α</mi><mo>(</mo><mi>G</mi><mo>)</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>(</mo><mi>H</mi><mo>)</mo></math>. By similar techniques, we prove sharp lower and upper bounds on the edge open packing number of the lexicographic product of graphs, which in particular lead to NP-hardness results in triangular graphs for both invariants studied in this paper. For the direct product <math><mi>G</mi><mo>×</mo><mi>H</mi></math> of two graphs we provide lower bounds on <math><msub><mrow><mi>ν</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>×</mo><mi>H</mi><mo>)</mo></math> and <math><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>e</mi></mrow><mrow><mi>o</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>×</mo><mi>H</mi><mo>)</mo></math>, both of which are widely sharp. We also present sharp lower bounds for both invariants in the Cartesian and the strong product of two graphs. Finally, we consider the edge open packing number in hypercubes establishing the exact values of <math><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>e</mi></mrow><mrow><mi>o</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math> when n is a power of 2, and present a closed formula for the induced matching number of the rooted product of arbitrary two graphs over an arbitrary root vertex.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114458"},"PeriodicalIF":0.7,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On HV-neighborhood group constant sum array 关于hv -邻域群常和数组

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-03 DOI: 10.1016/j.disc.2025.114456

Karthik S, Krishnan Paramasivam

{"title":"On HV-neighborhood group constant sum array","authors":"Karthik S, Krishnan Paramasivam","doi":"10.1016/j.disc.2025.114456","DOIUrl":"10.1016/j.disc.2025.114456","url":null,"abstract":"<div><div>A HV-neighborhood group constant sum array with δ distance, is an <math><mi>m</mi><mo>×</mo><mi>n</mi></math> array, whose entries are all non-zero elements of an additive Abelian group Γ such that the sum of group elements assigned to the δ-neighborhood of any cell <math><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math> in an <math><mi>m</mi><mo>×</mo><mi>n</mi></math> array is a unique element <math><mi>μ</mi><mo>∈</mo><mi>Γ</mi></math>, where the δ-neighborhood of a cell <math><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math> in an <math><mi>m</mi><mo>×</mo><mi>n</mi></math> array is the set of cells that are at most δ distance in the right, left, up, and down from <math><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math>, excluding the cell <math><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math>. The element μ is the neighborhood constant sum. In this article, we prove some necessary conditions for the existence of HV-neighborhood group constant sum arrays with δ distance. In addition, if <math><mi>δ</mi><mo>=</mo><mn>1</mn></math>, a method to construct HV-neighborhood group constant sum arrays and a characterization of HV-neighborhood Klein four-group constant sum arrays are given.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114456"},"PeriodicalIF":0.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143535039","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}

引用次数: 0

F2F2[u2]F2[u3]-additive cyclic codes are asymptotically good F2F2[u2]F2[u3]-加性循环码是渐近好的

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-03-03 DOI: 10.1016/j.disc.2025.114459

Hai Q. Dinh , Bhanu Pratap Yadav , Bac T. Nguyen , Ashish Kumar Upadhyay

引用次数: 0

Path eccentricity of k-AT-free graphs and application on graphs with the consecutive ones property 无k- at图的路径偏心率及其在连续图上的应用

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-02-28 DOI: 10.1016/j.disc.2025.114449

Paul Bastide , Claire Hilaire , Eileen Robinson

{"title":"Path eccentricity of k-AT-free graphs and application on graphs with the consecutive ones property","authors":"Paul Bastide , Claire Hilaire , Eileen Robinson","doi":"10.1016/j.disc.2025.114449","DOIUrl":"10.1016/j.disc.2025.114449","url":null,"abstract":"<div><div>The central path problem is a variation on the single facility location problem. The aim is to find, in a given connected graph G, a path P minimizing its eccentricity, which is the maximal distance from P to any vertex of the graph G. The path eccentricity of G is the minimal eccentricity achievable over all paths in G. In this article we consider the path eccentricity of the class of the k-AT-free graphs. They are graphs in which any set of three vertices contains a pair for which every path between them uses at least one vertex of the closed neighborhood at distance k of the third. We prove that they have path eccentricity bounded by k.</div><div>Moreover, we answer a question of Gómez and Gutiérrez asking if there is a relation between path eccentricity and the consecutive ones property. The latter is the property for a binary matrix to admit a permutation of the rows placing the 1's consecutively on the columns. It was already known that graphs whose adjacency matrices have the consecutive ones property have path eccentricity at most 1, and that the same remains true when the augmented adjacency matrices (with ones on the diagonal) have the consecutive ones property. We generalize these results as follow. We study graphs whose adjacency matrices can be made to satisfy the consecutive ones property after changing some values on the diagonal, and show that those graphs have path eccentricity at most 2, by showing that they are 2-AT-free.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114449"},"PeriodicalIF":0.7,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511942","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}

引用次数: 0