Discrete Applied Mathematics最新文献

{"title":"A quotient-lifting approach to the Hamiltonicity of the cylindrical 5-puzzle graph","authors":"Taizo Sadahiro","doi":"10.1016/j.dam.2026.01.031","DOIUrl":"10.1016/j.dam.2026.01.031","url":null,"abstract":"<div><div>In this short note, we construct an explicit Hamiltonian cycle in the state graph of the 5-puzzle on a cylindrical 2 × 3 grid, a graph with 720 vertices. The cycle is described by a short symbolic sequence of 48 moves over the alphabet <span><math><mrow><mo>{</mo><mstyle><mi>L</mi></mstyle><mo>,</mo><mstyle><mi>R</mi></mstyle><mo>,</mo><mstyle><mi>V</mi></mstyle><mo>}</mo></mrow></math></span>, repeated 15 times, which can be verified directly. We also find a shorter 24-move sequence whose repetition yields a 2-cycle cover, which can be spliced into a Hamiltonian path. These constructions arise naturally from a general method: lifting Hamiltonian cycles from a quotient graph under the action of the puzzle’s symmetry group. The method produces compact, human-readable cycle encoding.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"386 ","pages":"Pages 9-15"},"PeriodicalIF":1.0,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090450","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":"Edge general position in graphs: Graph products, integer linear programming and some applications","authors":"Zahra Hamed-Labbafian ,&nbsp;Michael A. Henning ,&nbsp;Mostafa Tavakoli","doi":"10.1016/j.dam.2026.01.008","DOIUrl":"10.1016/j.dam.2026.01.008","url":null,"abstract":"<div><div>An edge general position set in a graph <span><math><mi>G</mi></math></span> is a set of edges <span><math><mrow><mi>X</mi><mo>⊆</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> where no three distinct edges in <span><math><mi>X</mi></math></span> lie on a common shortest path. The edge general position number, denoted gp_e is the maximum cardinality of an edge general position set in <span><math><mi>G</mi></math></span>. In this study, we explore the edge general position number for various graph products, including the hierarchical product, corona product, and edge corona product. Additionally, we propose an integer linear programming model to address the edge general position problem.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"386 ","pages":"Pages 1-8"},"PeriodicalIF":1.0,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045207","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":"Cops and robbers on multi-layer graphs","authors":"Jessica Enright ,&nbsp;Kitty Meeks ,&nbsp;William Pettersson ,&nbsp;John Sylvester","doi":"10.1016/j.dam.2026.01.017","DOIUrl":"10.1016/j.dam.2026.01.017","url":null,"abstract":"<div><div>We generalise the popular <em>cops and robbers</em> game to multi-layer graphs, where each cop and the robber are restricted to a single layer (or set of edges). We demonstrate that initial intuition about the best way to allocate cops to layers is not always correct, and prove that the multi-layer cop number is neither bounded from above nor below by any increasing function of the cop numbers of the individual layers. We show that it is <span><math><mi>NP</mi></math></span>-hard to decide if <span><math><mi>k</mi></math></span> cops are sufficient to catch the robber, even if every cop layer is a tree and a set of isolated vertices. However, we give a polynomial time algorithm to determine if <span><math><mi>k</mi></math></span> cops can win when the robber layer is a tree. Additionally, we investigate a question of worst-case divisions of a simple graph into layers: given a simple graph <span><math><mi>G</mi></math></span>, what is the maximum number of cops required to catch a robber over all multi-layer graphs where each edge of <span><math><mi>G</mi></math></span> is in at least one layer and all layers are connected? For cliques, suitably dense random graphs, and graphs of bounded treewidth, we determine this parameter up to multiplicative constants. Lastly we consider a multi-layer variant of Meyniel’s conjecture, and show the existence of an infinite family of graphs whose multi-layer cop number is bounded from below by a constant times <span><math><mrow><mi>n</mi><mo>/</mo><mo>log</mo><mi>n</mi></mrow></math></span>, where <span><math><mi>n</mi></math></span> is the number of vertices in the graph.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 109-133"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090665","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":"Extremal oriented graphs avoiding 1-subdivision of an in-star","authors":"Zejun Huang,&nbsp;Chenxi Yang","doi":"10.1016/j.dam.2026.01.011","DOIUrl":"10.1016/j.dam.2026.01.011","url":null,"abstract":"<div><div>An oriented graph is a digraph obtained from an undirected graph by choosing an orientation for each edge. Given a positive integer <span><math><mi>n</mi></math></span> and an oriented graph <span><math><mi>F</mi></math></span>, the oriented Turán number <span><math><mrow><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>o</mi><mi>r</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>F</mi><mo>)</mo></mrow></mrow></math></span> is the maximum number of arcs in an <span><math><mi>F</mi></math></span>-free oriented graph of order <span><math><mi>n</mi></math></span>. In this paper, we investigate the oriented Turán number <span><math><mrow><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>o</mi><mi>r</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mover><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mrow><mo>⃗</mo></mover><mo>)</mo></mrow></mrow></math></span>, where <span><math><mover><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mrow><mo>⃗</mo></mover></math></span> is the 1-subdivision of the in-star of order <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span>. We determine <span><math><mrow><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>o</mi><mi>r</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mover><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mrow><mo>⃗</mo></mover><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span> as well as the extremal oriented graphs. For <span><math><mrow><mi>k</mi><mo>≥</mo><mn>4</mn></mrow></math></span>, we establish a lower bound and an upper bound on <span><math><mrow><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>o</mi><mi>r</mi><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mover><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mn>1</mn></mrow></msub></mrow><mo>⃗</mo></mover><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 134-145"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090577","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":"S-packing chromatic critical graphs","authors":"Gülnaz Boruzanlı Ekinci ,&nbsp;Csilla Bujtás ,&nbsp;Didem Gözüpek ,&nbsp;Sandi Klavžar","doi":"10.1016/j.dam.2026.01.024","DOIUrl":"10.1016/j.dam.2026.01.024","url":null,"abstract":"<div><div>For a non-decreasing sequence of positive integers <span><math><mrow><mi>S</mi><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>)</mo></mrow></mrow></math></span>, the <span><math><mi>S</mi></math></span>-packing chromatic number of a graph <span><math><mi>G</mi></math></span> is denoted by <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-critical graphs are introduced as the graphs <span><math><mi>G</mi></math></span> such that <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>&lt;</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> for each proper subgraph <span><math><mi>H</mi></math></span> of <span><math><mi>G</mi></math></span>. Several families of <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-critical graphs are constructed, and 2- and 3-colorable <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-critical graphs are presented for all packing sequences <span><math><mi>S</mi></math></span>, while 4-colorable <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-critical graphs are found for most of <span><math><mi>S</mi></math></span>. Cycles which are <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-critical are characterized under different conditions. It is proved that for any graph <span><math><mi>G</mi></math></span> and any edge <span><math><mrow><mi>e</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, the inequality <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mi>e</mi><mo>)</mo></mrow><mo>≥</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>/</mo><mn>2</mn></mrow></math></span> holds. Moreover, in several important cases, this bound can be improved to <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>−</mo><mi>e</mi><mo>)</mo></mrow><mo>≥</mo><mrow><mo>(</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn></mrow></math></span>. The sharpness of the bounds is also discussed. Along the way an earlier result on <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>S</mi></mrow></msub></math></span>-vertex-critical graphs is supplemented.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 77-85"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039497","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 generalized 3-connectivity of BCCC data center networks","authors":"Baohua Niu ,&nbsp;Yan Wang ,&nbsp;Hai Liu ,&nbsp;Baolei Cheng ,&nbsp;Jianxi Fan","doi":"10.1016/j.dam.2026.02.007","DOIUrl":"10.1016/j.dam.2026.02.007","url":null,"abstract":"<div><div>As the core infrastructure for technologies such as cloud computing, big data and artificial intelligence, data center networks (DCNs) realize efficient collaborative communication among massive servers, storage devices and terminal nodes through effective interconnection, reliable transmission and intelligent management mechanisms. In typical application scenarios like distributed computing, real-time business response and elastic resource expansion, the demand for multi-node collaborative communication is becoming more and more prominent. The traditional connectivity theory is limited to the analysis of connectivity between two nodes, which is difficult to adapt to the complex multi-node collaboration scenarios in data centers. To break this limitation, the concept of generalized connectivity based on the internally disjoint Steiner trees emerges as an important indicator to measure the connection strength among multiple nodes, which plays a significant role in characterizing the reliability and fault tolerance among multiple nodes. BCube connected crossbars (abbreviated as BCCC), a new server-centric DCN, exhibits superior network capabilities, including great scalability, low communication latency and high robustness to component failures. This work addresses the issue of packing internally disjoint Steiner trees in the logic graph of BCCC. Specifically, we determine the largest number of internally disjoint Steiner trees that connect arbitrary three nodes in the logic graph of BCCC, thereby deriving precise values of generalized 3-connectivity.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 165-177"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190150","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":"Disjunctive domination in maximal outerplanar graphs","authors":"Michael A. Henning ,&nbsp;Paras Vinubhai Maniya ,&nbsp;Dinabandhu Pradhan","doi":"10.1016/j.dam.2025.12.056","DOIUrl":"10.1016/j.dam.2025.12.056","url":null,"abstract":"<div><div>A disjunctive dominating set of a graph <span><math><mi>G</mi></math></span> is a set <span><math><mrow><mi>D</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> such that every vertex in <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>∖</mo><mi>D</mi></mrow></math></span> has a neighbor in <span><math><mi>D</mi></math></span> or has at least two vertices in <span><math><mi>D</mi></math></span> at distance 2 from it. The disjunctive domination number of <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>d</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is the minimum cardinality among all disjunctive dominating sets of <span><math><mi>G</mi></math></span>. In this paper, we show that if <span><math><mi>G</mi></math></span> is a maximal outerplanar graph of order <span><math><mrow><mi>n</mi><mo>≥</mo><mn>7</mn></mrow></math></span> with <span><math><mi>k</mi></math></span> vertices of degree 2, then <span><math><mrow><msubsup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>d</mi></mrow></msubsup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mrow><mo>⌊</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>9</mn></mrow></mfrac><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mi>k</mi><mo>)</mo></mrow><mo>⌋</mo></mrow></mrow></math></span>, and this bound is sharp.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 24-61"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039493","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":"Refinements of Combinatorial Nullstellensatz via polynomial supports","authors":"Wei Cao","doi":"10.1016/j.dam.2026.01.025","DOIUrl":"10.1016/j.dam.2026.01.025","url":null,"abstract":"<div><div>Nica introduced the notion of nullity for finite sets and utilized it to refine the Combinatorial Nullstellensatz over structured grids. Inspired by Nica’s approach, we replace the concept of nullity with the support of polynomials, thereby obtaining further refinements of the Combinatorial Nullstellensatz.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 62-64"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039496","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":"Games on deBruijn graphs and cycle means","authors":"Nadejda Drenska","doi":"10.1016/j.dam.2025.12.060","DOIUrl":"10.1016/j.dam.2025.12.060","url":null,"abstract":"<div><div>deBruijn graphs are widely used in genomics and computer science. In this paper we present a novel approach to finding weights on edges of doubly weighted deBruijn graphs. Given any fixed set of weights on vertices, we use a repeated two-person zero-sum game to find weights on edges so that every cycle on the deBruijn graph has the same average weight, providing explicit formulas. This approach uses minimax optimal strategies of the players. Once the weights on the edges are determined, we observe that they correspond to solving a set of linear equations with as many equations as there are cycles. This is very surprising, because there are many more cycles than unknowns. Moreover we analyze other, related games on graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 100-108"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039499","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":"Covering a supermodular-like function in a mixed hypergraph","authors":"Hui Gao","doi":"10.1016/j.dam.2026.01.023","DOIUrl":"10.1016/j.dam.2026.01.023","url":null,"abstract":"<div><div>In this paper, we solve a conjecture by Szigeti in [Matroid-rooted packing of arborescences], which characterizes mixed hypergraphs <span><math><mrow><mi>F</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>∪</mo><mi>A</mi><mo>)</mo></mrow></mrow></math></span> for which there exists an orientation <span><math><mover><mrow><mi>E</mi></mrow><mo>⃗</mo></mover></math></span> of <span><math><mi>E</mi></math></span> such that <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mover><mrow><mi>E</mi></mrow><mo>⃗</mo></mover><mo>∪</mo><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow><mo>≥</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>X</mi><mo>∈</mo><mi>P</mi></mrow></msub><mi>h</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>−</mo><mi>b</mi><mrow><mo>(</mo><mo>∪</mo><mi>P</mi><mo>)</mo></mrow></mrow></math></span> for every subpartition <span><math><mi>P</mi></math></span> of <span><math><mi>V</mi></math></span>, where <span><math><mi>h</mi></math></span> is an integer-valued, intersecting supermodular function on <span><math><mi>V</mi></math></span> and <span><math><mi>b</mi></math></span> a submodular function on <span><math><mi>V</mi></math></span>. As a corollary, another conjecture in the same paper is confirmed, which characterizes mixed hypergraphs admitting a packing of mixed hyperarborescences such that their roots form a basis in a given matroid, each vertex <span><math><mi>v</mi></math></span> belongs to exactly <span><math><mi>k</mi></math></span> of them and is the root of at least <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> and at most <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> of them.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"385 ","pages":"Pages 72-76"},"PeriodicalIF":1.0,"publicationDate":"2026-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039494","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}