Discrete Applied Mathematics最新文献

Comparing the p-independence number of regular graphs to the q-independence number of their line graphs 将正则图的p独立数与其线形图的q独立数进行比较

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-19 DOI: 10.1016/j.dam.2025.05.022

Yair Caro , Randy Davila , Ryan Pepper

引用次数: 0

A characterization of positive spanning sets with ties to strongly edge-connected digraphs 强边连通有向图的正生成集的刻画

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-19 DOI: 10.1016/j.dam.2025.05.025

Denis Cornaz, Sébastien Kerleau, Clément W. Royer

引用次数: 0

Tight conditions for spanning trees with leaf degree at most k in graphs 图中叶度最大为k的生成树的严密条件

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-18 DOI: 10.1016/j.dam.2025.05.016

Jifu Lin , Hechao Liu , Lihua You

引用次数: 0

Approximation algorithm for prize-collecting weighted set cover with fairness constraints 具有公平性约束的计奖加权集覆盖逼近算法

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-17 DOI: 10.1016/j.dam.2025.05.010

Mingchao Zhou, Zhao Zhang

{"title":"Approximation algorithm for prize-collecting weighted set cover with fairness constraints","authors":"Mingchao Zhou, Zhao Zhang","doi":"10.1016/j.dam.2025.05.010","DOIUrl":"10.1016/j.dam.2025.05.010","url":null,"abstract":"<div><div>Fairness has become one of the hottest concerns in recent research. This paper introduces the prize-collecting weighted set cover problem with fairness constraint (FPCWSC). It is a variant of the minimum weight set cover problem, in which every uncovered element incurs a penalty and the elements are divided into several groups, each group having a minimum number of elements required to be covered. The goal is to minimize the cost of selected sets plus the penalties on those uncovered elements, subject to the constraint that every group has its coverage requirement satisfied. We propose a four-phase algorithm using deterministic rounding twice, followed by a randomized rounding method and a greedy method. In polynomial time, the algorithm computes a feasible solution with an expected approximation ratio <math><mrow><mi>O</mi><mrow><mo>(</mo><mi>f</mi><mo>+</mo><mo>ln</mo><mi>Δ</mi><mo>)</mo></mrow></mrow></math>, where <math><mi>f</mi></math> is the maximum number of sets containing a common element and <math><mi>Δ</mi></math> is the maximum number of groups having nonempty intersection with a set.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 301-315"},"PeriodicalIF":1.0,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071809","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

Graceful colorings of graphs with maximum degree three 最大次为3的图的优美着色

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-17 DOI: 10.1016/j.dam.2025.05.013

Paola T. Pantoja , Simone Dantas , Atílio G. Luiz

{"title":"Graceful colorings of graphs with maximum degree three","authors":"Paola T. Pantoja , Simone Dantas , Atílio G. Luiz","doi":"10.1016/j.dam.2025.05.013","DOIUrl":"10.1016/j.dam.2025.05.013","url":null,"abstract":"<div><div>A graceful <math><mi>k</mi></math>-coloring of a graph <math><mi>G</mi></math> consists of a proper vertex coloring <math><mrow><mi>f</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> that induces a proper edge coloring. In this case, the color assigned to an edge <math><mrow><mi>u</mi><mi>v</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> is determined by the absolute value of the difference between the colors assigned to vertices <math><mi>u</mi></math> and <math><mi>v</mi></math>. The minimum <math><mi>k</mi></math> for which a graph <math><mi>G</mi></math> has a graceful <math><mi>k</mi></math>-coloring is the graceful chromatic number of <math><mi>G</mi></math>, denoted by <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math>. In this paper, we establish the first known upper bound for the graceful chromatic number of an arbitrary graph, in terms of its maximum degree <math><mi>Δ</mi></math>, i.e., we prove that the graceful chromatic number satisfies the inequality <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mfrac><mrow><mn>5</mn><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>3</mn><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>1</mn></mrow></math>. This result provides the first upper bound for <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>g</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math> of complete graphs <math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math>, and represents an improvement over a previous finding by Bi et al. (2017) for regular complete <math><mi>k</mi></math>-partite graphs <math><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></msub></math>. We demonstrate the <math><mi>NP</mi></math>-completeness of the problem of determining whether a graph <math><mi>G</mi></math> has a graceful 5-coloring. Furthermore, we extend our investigation to subcubic graphs, establishing upper bounds for the graceful chromatic number of families of subcubic graphs without adjacent vertices of maximum degree. Additionally, we determine the graceful chromatic number for two cubic graph classes, namely Flower snarks and Goldberg snarks.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"374 ","pages":"Pages 75-96"},"PeriodicalIF":1.0,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071491","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

Multi-word-representability of graphs 图的多字可表示性

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-17 DOI: 10.1016/j.dam.2025.05.021

Benny George Kenkireth, Gopalan Sajith, Sreyas Sasidharan

{"title":"Multi-word-representability of graphs","authors":"Benny George Kenkireth, Gopalan Sajith, Sreyas Sasidharan","doi":"10.1016/j.dam.2025.05.021","DOIUrl":"10.1016/j.dam.2025.05.021","url":null,"abstract":"<div><div>A graph <math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> is word-representable if there exists a word <math><mi>w</mi></math> over the alphabet <math><mi>V</mi></math> such that for any distinct pair of vertices <math><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>V</mi></mrow></math>, <math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>∈</mo><mi>E</mi></mrow></math> if and only if the occurrences of the letters <math><mi>x</mi></math> and <math><mi>y</mi></math> alternate in the word <math><mi>w</mi></math>. Word-representable graphs generalize many important graph classes such as 3-colorable graphs, comparability graphs, and graphs of vertex degree at most 3. The notion of multi-word representability of graphs is a generalization of the notion of word-representability. A graph <math><mi>G</mi></math> is <math><mi>k</mi></math>-multi-word-representable if it can be represented by a set of at most <math><mi>k</mi></math> words, each representing a word-representable subgraph of <math><mi>G</mi></math>, such that their union is <math><mi>G</mi></math>. 2-multi-word-representable graphs contain many graph classes, such as word-representable graphs, planar graphs, interval graphs, split graphs, and line graphs.</div><div>We first investigate the problem of finding the largest word-representable induced subgraph of a graph. We solve this problem for graphs of size up to nine. The second problem that we study is determining whether it is possible to vertex partition graphs on <math><mi>n</mi></math> vertices into two sets, each inducing a word-representable graph. We solve this problem for graphs of size up to thirteen and for perfect graphs of size up to sixteen. These results help us to show that graphs with at most 20 vertices are 2-multi-word-representable. The third problem we address involves computing the multi-word-representation number for certain subclasses of perfect graphs. In particular, our investigation reveals that perfect graphs with up to 28 vertices, well-partitioned chordal graphs, and <math><mrow><mo>(</mo><mn>6</mn><mo>+</mo><mi>y</mi><mo>)</mo></mrow></math>-trees with at most <math><mrow><mo>(</mo><mn>25</mn><mo>+</mo><mi>y</mi><mo>)</mo></mrow></math> vertices, all subclasses of perfect graphs, are 2-multi-word-representable. Additionally, we establish that any chordal graph is <math><mrow><mi>O</mi><mrow><mo>(</mo><mo>log</mo><mo>log</mo><mi>n</mi><mo>)</mo></mrow></mrow></math>-multi-word-representable.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"374 ","pages":"Pages 61-74"},"PeriodicalIF":1.0,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071484","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

A new locally t-diagnosable structure under the PMC model with an application to matching composition networks PMC模型下一种新的局部t可诊断结构及其在匹配组合网络中的应用

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-16 DOI: 10.1016/j.dam.2025.05.015

Meirun Chen , Cheng-Kuan Lin , Kung-Jui Pai

引用次数: 0

Hybrid intermittent fault diagnosis of general graphs 通用图的混合间歇故障诊断

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-15 DOI: 10.1016/j.dam.2025.05.009

Lulu Yang , Shuming Zhou , Weixing Zheng

{"title":"Hybrid intermittent fault diagnosis of general graphs","authors":"Lulu Yang , Shuming Zhou , Weixing Zheng","doi":"10.1016/j.dam.2025.05.009","DOIUrl":"10.1016/j.dam.2025.05.009","url":null,"abstract":"<div><div>With the rapid development of information technology, networks have emerged as a crucial infrastructure in the big data era. System-level fault diagnosis plays a vital role to locate and repair faulty nodes in networks. However, the majority of research primarily focus on diagnosing faulty nodes of regular networks, with comparably less attention devoted to fault identification in irregular networks under the circumstance of link failures. In this paper, we introduce the notion of hybrid intermittent fault diagnosability and derive the corresponding diagnosability for general networks. Additionally, we determine the hybrid intermittent fault diagnosability for various well-known networks. Furthermore, we propose a HIFPD-MM* algorithm, which possesses a time complexity of <math><mrow><mi>O</mi><mrow><mo>(</mo><mi>k</mi><mo>×</mo><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>|</mo></mrow><mi>⋅</mi><msup><mrow><mrow><mo>(</mo><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math>, where <math><mi>k</mi></math> denotes the number of stages of the algorithm in one round, and <math><mrow><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math> denotes the maximum degree of graph <math><mi>G</mi></math>. Through extensive experiments conducted on hypercubes and real-world datasets, we validate the effectiveness and accuracy of our proposed algorithm.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"374 ","pages":"Pages 16-32"},"PeriodicalIF":1.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948823","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

Forbidden pairs for 2-factorable and hamiltonian graphs under the necessary condition 二因子图和哈密顿图在必要条件下的禁止对

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-15 DOI: 10.1016/j.dam.2025.05.017

Qiang Wang , Liming Xiong

{"title":"Forbidden pairs for 2-factorable and hamiltonian graphs under the necessary condition","authors":"Qiang Wang , Liming Xiong","doi":"10.1016/j.dam.2025.05.017","DOIUrl":"10.1016/j.dam.2025.05.017","url":null,"abstract":"<div><div>In [1], Wang and Xiong characterize all forbidden pairs (not necessary connected) <math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math> such that 2-connected <math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math>-free graph <math><mi>G</mi></math> admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) <math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math> such that connected (or 2-edge-connected) <math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math>-free graph <math><mi>G</mi></math> admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) <math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math> such that connected (or 2-edge-connected) <math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math>-free graph <math><mi>G</mi></math> admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs <math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math> such that connected (or 2-edge-connected) <math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math>-free graph <math><mi>G</mi></math> who has an even-factor is hamiltonian.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 290-300"},"PeriodicalIF":1.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947461","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

Generalized saturation game 广义饱和对策

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-05-15 DOI: 10.1016/j.dam.2025.05.014

Balázs Patkós , Miloš Stojaković , Jelena Stratijev , Máté Vizer

{"title":"Generalized saturation game","authors":"Balázs Patkós , Miloš Stojaković , Jelena Stratijev , Máté Vizer","doi":"10.1016/j.dam.2025.05.014","DOIUrl":"10.1016/j.dam.2025.05.014","url":null,"abstract":"<div><div>We study the following game version of the generalized graph Turán problem. For two fixed graphs <math><mi>F</mi></math> and <math><mi>H</mi></math>, two players, Max and Mini, alternately claim unclaimed edges of the complete graph <math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></math> such that the graph <math><mi>G</mi></math> of the claimed edges must remain <math><mi>F</mi></math>-free throughout the game. The game ends when no further edges can be claimed, i.e. when <math><mi>G</mi></math> becomes <math><mi>F</mi></math>-saturated. The <math><mi>H</mi></math>-score of the game is the number of copies of <math><mi>H</mi></math> in <math><mi>G</mi></math>. Max aims to maximize the <math><mi>H</mi></math>-score, while Mini wants to minimize it. The <math><mi>H</mi></math>-score of the game when both players play optimally is denoted by <math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>#</mi><mi>H</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math> when Max starts, and by <math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>#</mi><mi>H</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math> when Mini starts. We study these values for several natural choices of <math><mi>F</mi></math> and <math><mi>H</mi></math>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"374 ","pages":"Pages 33-49"},"PeriodicalIF":1.0,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069361","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