Discrete Applied Mathematics最新文献_第10页

Generalized competitively orientable complete multipartite graphs 广义竞争可定向完全多部图

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.dam.2025.03.031

Myungho Choi

{"title":"Generalized competitively orientable complete multipartite graphs","authors":"Myungho Choi","doi":"10.1016/j.dam.2025.03.031","DOIUrl":"10.1016/j.dam.2025.03.031","url":null,"abstract":"<div><div>We say that a digraph <math><mi>D</mi></math> is <math><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></math>-step competitive if any two vertices have an <math><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></math>-step common out-neighbor in <math><mi>D</mi></math> and that a graph <math><mi>G</mi></math> is <math><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></math>-step competitively orientable if there exists an <math><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></math>-step competitive orientation of <math><mi>G</mi></math>.</div><div>In Choi et al. (2022), Choi et al. introduce the notion of the competitive digraph and completely characterize competitively orientable complete multipartite graphs in terms of the sizes of its partite sets. Here, a competitive digraph means a <math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math>-step competitive digraph. In this paper, the result of Choi et al. has been extended to a general characterization of <math><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></math>-step competitively orientable complete multipartite graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 65-72"},"PeriodicalIF":1.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715404","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

On irredundance coloring and irredundance compelling coloring of graphs 图的无冗余着色与无冗余强制着色

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.dam.2025.03.025

David Ashok Kalarkop , Michael A. Henning , Ismail Sahul Hamid , Pawaton Kaemawichanurat

{"title":"On irredundance coloring and irredundance compelling coloring of graphs","authors":"David Ashok Kalarkop , Michael A. Henning , Ismail Sahul Hamid , Pawaton Kaemawichanurat","doi":"10.1016/j.dam.2025.03.025","DOIUrl":"10.1016/j.dam.2025.03.025","url":null,"abstract":"<div><div>An irredundance coloring of a graph <math><mi>G</mi></math> is a proper coloring admitting a maximal irredundant set all of whose vertices receive different colors. The minimum number of colors required for an irredundance coloring of <math><mi>G</mi></math> is called the irredundance chromatic number of <math><mi>G</mi></math>, and is denoted by <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. An irredundance compelling coloring of <math><mi>G</mi></math> is a proper coloring of <math><mi>G</mi></math> in which every rainbow committee (a set consisting of one vertex of each color) is an irredundant set of <math><mi>G</mi></math>. The maximum number of colors required for an irredundance compelling coloring of <math><mi>G</mi></math> is called the irredundance compelling chromatic number of <math><mi>G</mi></math>, and is denoted by <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi><mi>r</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. We make a detailed study of <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi><mi>r</mi><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, derive bounds on these parameters and characterize extremal graphs attaining the bounds.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"369 ","pages":"Pages 149-161"},"PeriodicalIF":1.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715628","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

Measures of closeness to cordiality for graphs 图接近诚恳度的度量

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.dam.2025.03.012

Anand Brahmbhatt , Kartikeya Rai , Amitabha Tripathi

引用次数: 0

Some new bounds for the energy of graphs 图的能量的一些新界限

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.dam.2025.03.022

Jiuying Dong, Yingying Yao

{"title":"Some new bounds for the energy of graphs","authors":"Jiuying Dong, Yingying Yao","doi":"10.1016/j.dam.2025.03.022","DOIUrl":"10.1016/j.dam.2025.03.022","url":null,"abstract":"<div><div>Let <math><mi>G</mi></math> be a graph with <math><mi>n</mi></math> vertices and <math><mi>m</mi></math> edges. The energy of a graph <math><mi>G</mi></math> is defined as the sum of absolute values of the eigenvalues about its adjacency matrix, i.e. <math><mrow><mi>ɛ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow></mrow></math>. In this paper, we derive some new upper bounds on the graph energy based on a new formula and some inequalities for calculating the graph energy, and characterize the extremal graphs. In addition, we propose some new lower bounds for the graph energy involving order <math><mi>n</mi></math>, the size <math><mi>m</mi></math>, the eigenvalue with maximum absolute value <math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and the eigenvalue with minimum absolute value <math><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of the graph <math><mi>G</mi></math>, and characterize the extremal graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 73-79"},"PeriodicalIF":1.0,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715514","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

Preprocessing complexity for some graph problems parameterized by structural parameters 一类结构参数化图问题的预处理复杂度

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-25 DOI: 10.1016/j.dam.2025.03.023

Manuel Lafond, Weidong Luo

引用次数: 0

Bounds on the Aα-spectral radius of uniform hypergraphs with some vertices deleted 一些顶点被删除的一致超图的a α-谱半径的界

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-25 DOI: 10.1016/j.dam.2025.03.020

Peng-Li Zhang , Xiao-Dong Zhang

引用次数: 0

On disjunction convex hulls by big-M lifting 用大m提升法研究分离凸包

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-24 DOI: 10.1016/j.dam.2025.03.013

Yushan Qu, Jon Lee

{"title":"On disjunction convex hulls by big-M lifting","authors":"Yushan Qu, Jon Lee","doi":"10.1016/j.dam.2025.03.013","DOIUrl":"10.1016/j.dam.2025.03.013","url":null,"abstract":"<div><div>We study the natural extended-variable formulation for the disjunction of <math><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></math> polytopes in <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math>. We demonstrate that the convex hull <math><mi>D</mi></math> in the natural extended-variable space <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mi>n</mi></mrow></msup></math> is given by full optimal big-M lifting (i) when <math><mrow><mi>d</mi><mo>≤</mo><mn>2</mn></mrow></math> (and that it is not generally true for <math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math>), and also (ii) under some technical conditions, when the polytopes have a common facet-describing constraint matrix, for arbitrary <math><mrow><mi>d</mi><mo>≥</mo><mn>1</mn></mrow></math> and <math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math>. We give a broad family of examples with <math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math> and <math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math>, where the convex hull is not described after employing all full optimal big-M lifting inequalities, but it is described after one round of MIR inequalities. Additionally, we give some general results on the polyhedral structure of <math><mi>D</mi></math>, and we demonstrate that all facets of <math><mi>D</mi></math> can be enumerated in polynomial time when <math><mi>d</mi></math> is fixed.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 31-45"},"PeriodicalIF":1.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683253","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

Grundy packing coloring of graphs 图形的Grundy填充着色

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-24 DOI: 10.1016/j.dam.2025.03.024

Didem Gözüpek , Iztok Peterin

{"title":"Grundy packing coloring of graphs","authors":"Didem Gözüpek , Iztok Peterin","doi":"10.1016/j.dam.2025.03.024","DOIUrl":"10.1016/j.dam.2025.03.024","url":null,"abstract":"<div><div>A map <math><mrow><mi>c</mi><mo>:</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>→</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></mrow></math> of a graph <math><mi>G</mi></math> is a packing <math><mi>k</mi></math>-coloring if every two different vertices of the same color <math><mrow><mi>i</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></mrow></math> are at distance more than <math><mi>i</mi></math>. The packing chromatic number <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> of <math><mi>G</mi></math> is the smallest integer <math><mi>k</mi></math> such that there exists a packing <math><mi>k</mi></math>-coloring. In this paper we introduce the notion of Grundy packing chromatic number, analogous to the Grundy chromatic number of a graph. We first present a polynomial-time algorithm that is based on a greedy approach and gives a packing coloring of any graph <math><mi>G</mi></math>. We then define the Grundy packing chromatic number <math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> of a graph <math><mi>G</mi></math> as the maximum value that this algorithm yields in <math><mi>G</mi></math>. We present several properties of <math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>, provide results on the complexity of the problem as well as bounds and some exact results for <math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 17-30"},"PeriodicalIF":1.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683268","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

Pareto-scheduling of two competing agents with total weighted tardiness being one criterion 以总加权延迟为一个标准的两个竞争代理的帕累托调度

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-24 DOI: 10.1016/j.dam.2025.03.026

Jinwen Sun , Rubing Chen , Qiulan Zhao

引用次数: 0

The planar Turán number of double stars S2,l 双星S2, 1的平面Turán数

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-03-22 DOI: 10.1016/j.dam.2025.03.016

Xin Xu , Jiawei Shao , Qiang Zhou

引用次数: 0