Discrete Applied Mathematics最新文献

{"title":"Berge coalitional stabilities in the graph model for conflict resolution","authors":"Giannini Italino Alves Vieira ,&nbsp;Leandro Chaves Rêgo","doi":"10.1016/j.dam.2025.09.012","DOIUrl":"10.1016/j.dam.2025.09.012","url":null,"abstract":"<div><div>Altruism is a behavior that is commonly observed in human interactions. The concept of Berge stability has been introduced in game theory and, more recently, in the graph model for conflict resolution, to represent decision makers (DMs) that act altruistically expecting others to reciprocate. However, this stability concept has only been introduced from the point of view of individual DMs. This paper incorporates the concept of Berge stability into the framework of coalition analysis within the graph model for conflict resolution. In particular, it introduces nine novel concepts for coalition analysis and thoroughly examines the relationships among these new concepts, as well as their connections to other coalition concepts found in the existing literature on this model. To illustrate the use in practice of the proposed stability concepts, a coalitional Berge stability analysis is conducted in the Elmira groundwater contamination conflict.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 405-418"},"PeriodicalIF":1.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105087","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}

{"title":"Odd coloring of 2-boundary planar graphs and beyond","authors":"Weichan Liu ,&nbsp;Mengke Qi ,&nbsp;Xin Zhang","doi":"10.1016/j.dam.2025.08.064","DOIUrl":"10.1016/j.dam.2025.08.064","url":null,"abstract":"<div><div>In this paper, we introduce the notion of 2-boundary planar graphs. A graph is 2-boundary planar if it has an embedding in the plane so that all vertices lie on the boundary of at most two faces and no edges are crossed. A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. Petruševski and Škrekovski conjectured in 2022 that every planar graph admits an odd 5-coloring. We confirm this conjecture for 2-boundary planar graphs. Moreover, we present several questions regarding 2-boundary planar graphs that are of independent interest.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 68-79"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097643","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}

{"title":"The maximum number of cliques in graphs with given fractional matching number and minimum degree","authors":"Chengli Li,&nbsp;Yurui Tang","doi":"10.1016/j.dam.2025.09.010","DOIUrl":"10.1016/j.dam.2025.09.010","url":null,"abstract":"<div><div>Recently, Ma, Qian and Shi determined the maximum size of an <span><math><mi>n</mi></math></span>-vertex graph with given fractional matching number <span><math><mi>s</mi></math></span> and maximum degree at most <span><math><mi>d</mi></math></span>. Motivated by this result, we determine the maximum number of <span><math><mi>ℓ</mi></math></span>-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma’s result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 390-399"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105088","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}

{"title":"Single machine scheduling with a restricted rate-modifying activity to minimize the weighted makespan","authors":"Lili Zuo,&nbsp;Jing Zhang,&nbsp;Zhan Shi,&nbsp;Bingbing Fan","doi":"10.1016/j.dam.2025.09.013","DOIUrl":"10.1016/j.dam.2025.09.013","url":null,"abstract":"<div><div>We investigate the single machine scheduling problem with a restricted rate-modifying activity (RMA) aimed at minimizing the weighted makespan. The RMA is an activity that modifies the machine’s production rate while occupying it for a specified duration. Importantly, its starting time is constrained to fall within a predetermined interval <span><math><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></math></span>. Our results demonstrate that the special case where parameter <span><math><mrow><mi>a</mi><mo>=</mo><mn>0</mn></mrow></math></span> admits a polynomial-time solution, while the cases with <span><math><mrow><mi>b</mi><mo>=</mo><mi>∞</mi></mrow></math></span> or <span><math><mrow><mi>b</mi><mo>=</mo><mi>a</mi></mrow></math></span> are proven to be binary NP-hard. For these NP-hard problems, we develop pseudo-polynomial time dynamic programming solutions. Notably, in the scenario where splitting is permitted, we establish a polynomial-time algorithm for the <span><math><mrow><mi>b</mi><mo>=</mo><mi>a</mi></mrow></math></span> case, which in turn enables the derivation of a 2-approximation algorithm for the non-split version. Additionally, by combining our dynamic programming approach with the vector trimming technique, we achieve fully polynomial-time approximation schemes (FPTAS) for all NP-hard variants under consideration.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 89-100"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097617","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}

{"title":"On sign-invertible graphs","authors":"Isaiah Osborne ,&nbsp;Dong Ye","doi":"10.1016/j.dam.2025.09.005","DOIUrl":"10.1016/j.dam.2025.09.005","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a graph and <span><math><mi>A</mi></math></span> be its adjacency matrix. A graph <span><math><mi>G</mi></math></span> is invertible if its adjacency matrix <span><math><mi>A</mi></math></span> is invertible and the inverse of <span><math><mi>G</mi></math></span> is a weighted graph with adjacency matrix <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>. A signed graph <span><math><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>σ</mi><mo>)</mo></mrow></math></span> is a weighted graph with a special weight function <span><math><mrow><mi>σ</mi><mo>:</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>→</mo><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span>. A graph is sign-invertible if its inverse is a signed graph. A sign-invertible graph is always unimodular. The inverses of graphs have interesting combinatorial interests. In this paper, we study inverses of graphs and provide a combinatorial description for sign-invertible graphs, which provides a tool to characterize sign-invertible graphs. As applications, we completely characterize sign-invertible bipartite graphs with a unique perfect matching, and sign-invertible graphs with cycle rank at most two. As corollaries of these characterizations, some early results on trees (Buckley, Doty and Harary in 1982) and unicyclic graphs with a unique perfect matching (Kalita and Sarma in 2022) follow directly.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 101-115"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097644","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}

{"title":"Interlacing properties of Laplacian eigenvalues of chain graphs","authors":"Milica Anđelić ,&nbsp;Zoran Stanić ,&nbsp;Fernando C. Tura","doi":"10.1016/j.dam.2025.09.007","DOIUrl":"10.1016/j.dam.2025.09.007","url":null,"abstract":"<div><div>Chain graphs are <span><math><mrow><mo>{</mo><mn>2</mn><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>}</mo></mrow></math></span>-free graphs. The Laplacian spectrum of a chain graph of order <span><math><mi>n</mi></math></span> consists of <span><math><mrow><mi>n</mi><mo>−</mo><mn>2</mn><mi>h</mi></mrow></math></span> integer eigenvalues and <span><math><mrow><mn>2</mn><mi>h</mi></mrow></math></span> possibly non-integer eigenvalues that correspond to the associated quotient matrix of order <span><math><mrow><mn>2</mn><mi>h</mi></mrow></math></span>. We show that <span><math><mrow><mn>2</mn><mi>h</mi></mrow></math></span> complementary eigenvalues interlace vertex degrees. As an application, we confirm that the Brouwer’s conjecture holds for chain graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 80-88"},"PeriodicalIF":1.0,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061296","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}

{"title":"Minimized compact automaton for clumps over degenerate patterns","authors":"E. Furletova ,&nbsp;J. Holub ,&nbsp;M. Régnier","doi":"10.1016/j.dam.2025.08.049","DOIUrl":"10.1016/j.dam.2025.08.049","url":null,"abstract":"<div><div>Clumps are sequences of overlapping occurrences of a given pattern that play a vital role in the study of distribution of pattern occurrences. These distributions are used for finding functional fragments in biological sequences. In this paper we present a minimized compacted automaton (Overlap walking automaton, <em>OWA</em>) recognizing all the possible clumps for degenerate patterns and its usage for computation of probabilities of sets of clumps. We also present <span>Aho–Corasick</span> like automaton, <em>RMinPatAut</em>, recognizing all the sequences ending with pattern occurrences. The states of <em>RMinPatAut</em> are equivalence classes on the prefixes of the pattern words. We use <em>RMinPatAut</em> as an auxiliary structure for <em>OWA</em> construction. For degenerate patterns, <em>RMinPatAut</em> is Nerode-minimal, i.e., minimal in classical sense. In this case <em>RMinPatAut</em> can be constructed in linear time on the number of its states (it is bounded by <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup></math></span>, where <span><math><mi>m</mi></math></span> the length of pattern words). <em>OWA</em> can be constructed in linear time on the sum of its size and <em>RMinPatAut</em> size.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 51-67"},"PeriodicalIF":1.0,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061295","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}

{"title":"An approximate dynamic programming approach for multi-stage stochastic lot-sizing under a Decision–Hazard–Decision information structure","authors":"Victor Spitzer ,&nbsp;Céline Gicquel ,&nbsp;Evgeny Gurevsky ,&nbsp;François Sanson","doi":"10.1016/j.dam.2025.08.051","DOIUrl":"10.1016/j.dam.2025.08.051","url":null,"abstract":"<div><div>This work studies a combinatorial optimization problem encountered in industrial production planning: the single-item multi-resource lot-sizing problem with inventory bounds and lost sales. The demand to be satisfied by the production plan is subject to uncertainty and only probabilistically known. We consider a multi-stage decision process with a Decision–Hazard–Decision information structure in which decisions are made at each stage both before and after the uncertainty is revealed. Such a setting has not yet been studied for stochastic lot-sizing problems, and the resulting problem is modeled as a multi-stage stochastic integer program. We propose a solution approach based on an approximate stochastic dynamic programming algorithm. It relies on a decomposition of the problem into single-stage sub-problems and on the estimation at each stage of the expected future costs. Due to the Decision–Hazard–Decision information structure, each nested single-stage sub-problem is itself a two-stage stochastic integer program. We therefore introduce a Benders decomposition scheme to reduce the computational effort required to solve each nested sub-problem, and present a special-purpose polynomial-time algorithm to efficiently solve the single-scenario second-stage sub-problems involved in the Benders decomposition. The results of extensive simulation experiments carried out on large-size randomly generated instances are reported. They demonstrate the practical benefit, in terms of the actual production cost, of using the proposed approach as compared to a naive deterministic optimization approach based on the expected demand.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 355-378"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049050","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}

{"title":"Hardness transitions of star colouring and restricted star colouring","authors":"Shalu M.A. ,&nbsp;Cyriac Antony","doi":"10.1016/j.dam.2025.08.056","DOIUrl":"10.1016/j.dam.2025.08.056","url":null,"abstract":"<div><div>We study how the complexity of the graph colouring problems star colouring and restricted star colouring vary with the maximum degree of the graph. Restricted star colouring (in short, rs colouring) is a variant of star colouring, as the name implies. For <span><math><mrow><mi>k</mi><mo>∈</mo><mi>N</mi></mrow></math></span>, a <span><math><mi>k</mi></math></span>-colouring of a graph <span><math><mi>G</mi></math></span> is a function <span><math><mrow><mi>f</mi><mo>:</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>→</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math></span> such that <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≠</mo><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> for every edge <span><math><mrow><mi>u</mi><mi>v</mi></mrow></math></span> of <span><math><mi>G</mi></math></span>. A <span><math><mi>k</mi></math></span>-colouring of <span><math><mi>G</mi></math></span> is called a <span><math><mi>k</mi></math></span>-star colouring of <span><math><mi>G</mi></math></span> if there is no path <span><math><mrow><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>x</mi></mrow></math></span> in <span><math><mi>G</mi></math></span> with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. A <span><math><mi>k</mi></math></span>-colouring of <span><math><mi>G</mi></math></span> is called a <span><math><mi>k</mi></math></span>-rs colouring of <span><math><mi>G</mi></math></span> if there is no path <span><math><mrow><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi></mrow></math></span> in <span><math><mi>G</mi></math></span> with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>&gt;</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow></mrow></math></span>. For <span><math><mrow><mi>k</mi><mo>∈</mo><mi>N</mi></mrow></math></span>, the problem <span><math><mi>k</mi></math></span>-<span>Star Colourability</span> takes a graph <span><math><mi>G</mi></math></span> as input and asks whether <span><math><mi>G</mi></math></span> admits a <span><math><mi>k</mi></math></span>-star colouring. The problem <span><math><mi>k</mi></math></span>-RS <span>Colourability</span> is defined similarly. Recently, Brause et al. (Electron. J. Comb., 2022) investigated the complexity of 3-star colouring with respect to the graph diameter. We study the complexity of <span><math><mi>k</mi></math></span>-star colouring and <span><math><mi>k</mi></math></span>-rs colouring with respect to the maximum degree for all <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. For <span><math><mr","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 1-33"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050667","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}

{"title":"Maximal polyomino chains with respect to the Kirchhoff index","authors":"Wensheng Sun ,&nbsp;Yujun Yang ,&nbsp;Shou-Jun Xu","doi":"10.1016/j.dam.2025.08.060","DOIUrl":"10.1016/j.dam.2025.08.060","url":null,"abstract":"<div><div>Let <span><math><mi>G</mi></math></span> be a connected graph. The resistance distance between two vertices <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> of <span><math><mi>G</mi></math></span> is defined as the potential difference generated between <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> induced by the unique <span><math><mrow><mi>u</mi><mo>→</mo><mi>v</mi></mrow></math></span> flow when a unit current flows in from node <span><math><mi>u</mi></math></span> and flows out from node <span><math><mi>v</mi></math></span>. The Kirchhoff index of <span><math><mi>G</mi></math></span> is defined as the sum of all the resistance distances pairs of <span><math><mi>G</mi></math></span>. Polyomino chains, as an important geometric structure, have been widely studied in statistical physics and mathematical chemistry. In this paper, by employing standard techniques from electrical networks and using comparison results on the Kirchhoff index of <span><math><mrow><mi>S</mi><mo>,</mo><mi>T</mi></mrow></math></span>-isomers, we first show that among all polyomino chains with <span><math><mi>n</mi></math></span> squares, the maximum Kirchhoff index is attained only when the polyomino chain is a “bend-free” chain. Furthermore, according to the recursion formula for the resistance distances, “bend-free” chains with maximum and minimum Kirchhoff index are characterized. As a result, the polyomino chains with maximum Kirchhoff index are obtained.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 34-50"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050666","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}