Discrete Applied Mathematics最新文献_第10页

Spanning trees of bipartite graphs with a bounded number of leaves and branch vertices

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-12 DOI: 10.1016/j.dam.2024.12.004

Xinyu Huang, Zheng Yan

引用次数: 0

The degree sequence of the preferential attachment model

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-12 DOI: 10.1016/j.dam.2024.11.035

Lu Yu

引用次数: 0

The ɛ-spectral radius of trees with perfect matchings

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-12 DOI: 10.1016/j.dam.2024.11.028

Lu Huang, Aimei Yu, Rong-Xia Hao

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Games restricted by simplicial complexes and an application to vertiport cooperation

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-10 DOI: 10.1016/j.dam.2024.11.033

A. Jiménez-Losada, M. Ordóñez-Sánchez, J.C. Rodríguez-Gómez

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Upper bounds and approximation results for the k-slow burning problem

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-09 DOI: 10.1016/j.dam.2024.11.025

Michaela Hiller , Arie M.C.A. Koster , Philipp Pabst

{"title":"Upper bounds and approximation results for the k-slow burning problem","authors":"Michaela Hiller , Arie M.C.A. Koster , Philipp Pabst","doi":"10.1016/j.dam.2024.11.025","DOIUrl":"10.1016/j.dam.2024.11.025","url":null,"abstract":"<div><div><span><math><mi>k</mi></math></span>-slow burning is a model for contagion in social networks. In this model, given an undirected graph <span><math><mi>G</mi></math></span> in every time step, first every burning vertex spreads the fire to up to <span><math><mi>k</mi></math></span> of its neighbours, before second one additional source of fire is ignited. The <span><math><mi>k</mi></math></span>-slow burning number, denoted by <span><math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is the minimum number of time steps needed until the whole graph is burning. This model can be seen as a combination of the classic graph burning problem and the much older (<span><math><mi>k</mi></math></span>-)broadcasting problem. We prove <span><math><mi>NP</mi></math></span>-hardness of the <span><math><mi>k</mi></math></span>-slow burning problem for every fixed <span><math><mi>k</mi></math></span> on path forests, spider graphs and most notably the class of graphs of radius 1, where normal graph burning is solvable in polynomial time. Furthermore, we show that among all connected graphs on <span><math><mi>n</mi></math></span> vertices, the <span><math><mi>k</mi></math></span>-slow burning number of the star graph, <span><math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>s</mi></mrow></msub><mrow><mo>(</mo><mi>k</mi><mo>,</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>)</mo></mrow></mrow></math></span>, is maximal for <span><math><mrow><mi>k</mi><mo>∈</mo><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow></mrow></math></span> and asymptotically maximal for fixed <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. This observation motivates a generalisation of the burning number conjecture for <span><math><mi>k</mi></math></span>-slow burning. Finally, we give a <span><math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math></span>-approximation for the <span><math><mi>k</mi></math></span>-slow burning problem on path forests and a 2-approximation on trees.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"363 ","pages":"Pages 88-104"},"PeriodicalIF":1.0,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098697","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

List recoloring of planar graphs

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-07 DOI: 10.1016/j.dam.2024.11.031

L. Sunil Chandran , Uttam K. Gupta , Dinabandhu Pradhan

引用次数: 0

The clique number of the exact distance t-power graph: Complexity and eigenvalue bounds

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-06 DOI: 10.1016/j.dam.2024.11.032

Aida Abiad, Afrouz Jabal Ameli, Luuk Reijnders

{"title":"The clique number of the exact distance t-power graph: Complexity and eigenvalue bounds","authors":"Aida Abiad, Afrouz Jabal Ameli, Luuk Reijnders","doi":"10.1016/j.dam.2024.11.032","DOIUrl":"10.1016/j.dam.2024.11.032","url":null,"abstract":"<div><div>The exact distance <span><math><mi>t</mi></math></span>-power of a graph <span><math><mi>G</mi></math></span>, <span><math><msup><mrow><mi>G</mi></mrow><mrow><mrow><mo>[</mo><mi>♯</mi><mi>t</mi><mo>]</mo></mrow></mrow></msup></math></span>, is a graph which has the same vertex set as <span><math><mi>G</mi></math></span>, with two vertices adjacent in <span><math><msup><mrow><mi>G</mi></mrow><mrow><mrow><mo>[</mo><mi>♯</mi><mi>t</mi><mo>]</mo></mrow></mrow></msup></math></span> if and only if they are at distance exactly <span><math><mi>t</mi></math></span> in the original graph <span><math><mi>G</mi></math></span>. We study the clique number of this graph, also known as the <span><math><mi>t</mi></math></span>-equidistant number. We show that it is NP-hard to determine the <span><math><mi>t</mi></math></span>-equidistant number of a graph, and that in fact, it is NP-hard to approximate it within a constant factor. We also investigate how the <span><math><mi>t</mi></math></span>-equidistant number relates to another distance-based graph parameter; the <span><math><mi>t</mi></math></span>-independence number. In particular, we show how large the gap between both parameters can be. The hardness results motivate deriving eigenvalue bounds, which compare well against a known general bound. In addition, the tightness of the proposed eigenvalue bounds is studied.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"363 ","pages":"Pages 55-70"},"PeriodicalIF":1.0,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098683","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

Computing the minimal perimeter polygon for digital objects in the triangular tiling

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-03 DOI: 10.1016/j.dam.2024.11.026

Petra Wiederhold

{"title":"Computing the minimal perimeter polygon for digital objects in the triangular tiling","authors":"Petra Wiederhold","doi":"10.1016/j.dam.2024.11.026","DOIUrl":"10.1016/j.dam.2024.11.026","url":null,"abstract":"<div><div>This work presents an algorithm, together with its correctness proof, to determine the minimum perimeter polygon (MPP) for digital objects given as regular complexes in the triangular plane tiling. Such objects are edge-adjacency-connected sets of triangle tiles that have no end tiles, and the point set union of all their tiles forms a simple polygon. Nevertheless, the boundary paths of the objects are not assumed to be simple. Then the MPP is a weakly simple polygon that coincides with the relative convex hull (i.e., geodesic hull) of a set <span><math><mi>A</mi></math></span> with respect to a simple polygon <span><math><mi>B</mi></math></span>, where <span><math><mrow><mi>A</mi><mo>⊂</mo><mi>B</mi></mrow></math></span>, but <span><math><mi>A</mi></math></span> is not necessarily a polygon, in fact it is generally not connected. Our MPP algorithm relies on constructing and iteratively constraining cones of visibility through forthcoming boundary tiles, it uses the structure of the canonical boundary path, the MPP frontier is the shortest polygonal curve following this path. We also propose a boundary tracing algorithm to obtain such paths from the objects.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"363 ","pages":"Pages 27-44"},"PeriodicalIF":1.0,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098682","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

Small matchings extend to Hamiltonian cycles in hypercubes with disjoint faulty edges

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-02 DOI: 10.1016/j.dam.2024.11.030

Fan Wang

{"title":"Small matchings extend to Hamiltonian cycles in hypercubes with disjoint faulty edges","authors":"Fan Wang","doi":"10.1016/j.dam.2024.11.030","DOIUrl":"10.1016/j.dam.2024.11.030","url":null,"abstract":"<div><div>Fault tolerance is an important indicator for measuring network stability. Usually, we hope to ensure the normal transmission of information and data in the event of partial failures in the network, which requires the network to have a certain degree of fault tolerance. The hypercube <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is one of the most popular and efficient interconnection networks. We consider the question of a matching extending to a Hamiltonian cycle in <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> with disjoint faulty edges, and obtain the following result. For <span><math><mrow><mi>n</mi><mo>≥</mo><mn>5</mn></mrow></math></span>, let <span><math><mi>M</mi></math></span> be a matching of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, and <span><math><mi>F</mi></math></span> be a matching of <span><math><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>M</mi></mrow></math></span> such that <span><math><mrow><mrow><mo>|</mo><mi>M</mi><mo>|</mo></mrow><mo>+</mo><mrow><mo>|</mo><mi>F</mi><mo>|</mo></mrow><mo>≤</mo><mn>3</mn><mi>n</mi><mo>−</mo><mn>12</mn></mrow></math></span>. Then there exists a Hamiltonian cycle containing <span><math><mi>M</mi></math></span> in <span><math><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>F</mi></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"363 ","pages":"Pages 16-26"},"PeriodicalIF":1.0,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143099012","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

Twin-width of graphs with tree-structured decompositions

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-12-02 DOI: 10.1016/j.dam.2024.11.029

Irene Heinrich, Simon Raßmann

{"title":"Twin-width of graphs with tree-structured decompositions","authors":"Irene Heinrich, Simon Raßmann","doi":"10.1016/j.dam.2024.11.029","DOIUrl":"10.1016/j.dam.2024.11.029","url":null,"abstract":"<div><div>The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 (Bonnet et al., 2022), a mass of new results has appeared relating twin-width to group theory, model theory, combinatorial optimization, and structural graph theory.</div><div>We take a detailed look at the interplay between the twin-width of a graph and the twin-width of its components under tree-structured decompositions: We prove that the twin-width of a graph of strong tree-width <span><math><mi>k</mi></math></span> is at most <span><math><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>k</mi><mo>+</mo><mi>o</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>, contrasting nicely with the result of Bonnet and Déprés (2023), which states that twin-width can be exponential in tree-width. Further, we employ the fundamental concept from structural graph theory of decomposing a graph into highly connected components, in order to obtain optimal linear bounds on the twin-width of a graph given the widths of its biconnected components. For triconnected components we obtain a linear upper bound if we add red edges to the components indicating the splits which led to the components. Extending this approach to quasi-4-connectivity, we obtain a quadratic upper bound. Finally, we investigate how the adhesion of a tree decomposition influences the twin-width of the decomposed graph.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"363 ","pages":"Pages 1-15"},"PeriodicalIF":1.0,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098685","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