Discrete Applied Mathematics最新文献

Identification of a monotone Boolean function with k “reasons” as a combinatorial search problem 具有k个“原因”的单调布尔函数的识别作为一个组合搜索问题

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-10-04 DOI: 10.1016/j.dam.2025.09.028

Dániel Gerbner , András Imolay , Gyula O.H. Katona , Dániel T. Nagy , Kartal Nagy , Balázs Patkós , Domonkos Stadler , Kristóf Zólomy

{"title":"Identification of a monotone Boolean function with k “reasons” as a combinatorial search problem","authors":"Dániel Gerbner , András Imolay , Gyula O.H. Katona , Dániel T. Nagy , Kartal Nagy , Balázs Patkós , Domonkos Stadler , Kristóf Zólomy","doi":"10.1016/j.dam.2025.09.028","DOIUrl":"10.1016/j.dam.2025.09.028","url":null,"abstract":"<div><div>We study the number of queries needed to identify a monotone Boolean function <math><mrow><mi>f</mi><mo>:</mo><msup><mrow><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mrow></math>. A query consists of a 0-1-sequence, and the answer is the value of <math><mi>f</mi></math> on that sequence. It is well-known that the number of queries needed is <math><mrow><mfenced><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mrow><mo>⌊</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></mrow></mfrac></mrow></mfenced><mo>+</mo><mfenced><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mrow><mo>⌊</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced></mrow></math> in general. Here we study a variant where <math><mi>f</mi></math> has <math><mi>k</mi></math> “reasons” to be 1, i.e., its disjunctive normal form has <math><mi>k</mi></math> conjunctions if the redundant conjunctions are deleted. This problem is equivalent to identifying an upfamily in <math><msup><mrow><mn>2</mn></mrow><mrow><mrow><mo>[</mo><mi>n</mi><mo>]</mo></mrow></mrow></msup></math> that has exactly <math><mi>k</mi></math> minimal members. We find the asymptotics on the number of queries needed for fixed <math><mi>k</mi></math>. We also study the non-adaptive version of the problem, where the queries are asked at the same time, and determine the exact number of queries for most values of <math><mi>k</mi></math> and <math><mi>n</mi></math>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 703-709"},"PeriodicalIF":1.0,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218960","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 Poisson limit for the number of sub-matrices of random binary matrices satisfying the majority rule 满足多数原则的随机二值矩阵的子矩阵数的泊松极限

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-10-03 DOI: 10.1016/j.dam.2025.09.004

Italo Simonelli , Andreas Wendemuth

引用次数: 0

Construction of regular homogeneously traceable nonhamiltonian graphs 正则齐次可追踪非哈密顿图的构造

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-30 DOI: 10.1016/j.dam.2025.08.052

Xining Liu, Pu Qiao

{"title":"Construction of regular homogeneously traceable nonhamiltonian graphs","authors":"Xining Liu, Pu Qiao","doi":"10.1016/j.dam.2025.08.052","DOIUrl":"10.1016/j.dam.2025.08.052","url":null,"abstract":"<div><div>A graph is called homogeneously traceable if every vertex is an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for every integer <math><mrow><mi>n</mi><mo>≥</mo><mn>9</mn><mo>,</mo></mrow></math> there exists a homogeneously traceable nonhamiltonian graph of order <math><mi>n</mi></math>. The graphs they constructed are irregular. Thus it is natural to consider the existence problem of regular homogeneously traceable nonhamiltonian graphs. In 2022 Hu and Zhan proved that for every even integer <math><mrow><mi>n</mi><mo>≥</mo><mn>10</mn></mrow></math>, there exists a cubic homogeneously traceable nonhamiltonian graph of order <math><mi>n</mi></math>, and for every integer <math><mrow><mi>n</mi><mo>≥</mo><mn>18</mn></mrow></math>, there exists a 4-regular homogeneously traceable nonhamiltonian graph of order <math><mi>n</mi></math>. They also posed the problem: Given an integer <math><mrow><mi>k</mi><mo>≥</mo><mn>4</mn></mrow></math>, determine the integers <math><mi>n</mi></math> such that there exists a <math><mi>k</mi></math>-regular homogeneously traceable nonhamiltonian graph of order <math><mi>n</mi></math>. We prove two results: (1) For every odd integer <math><mrow><mi>k</mi><mo>≥</mo><mn>5</mn></mrow></math>, integer <math><mrow><mi>p</mi><mo>≥</mo><mn>6</mn></mrow></math> and integer <math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>}</mo></mrow></mrow></math>, there exists a <math><mi>k</mi></math>-regular homogeneously traceable nonhamiltonian graph of order <math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>q</mi></mrow></math>; (2) for every even integer <math><mrow><mi>k</mi><mo>≥</mo><mn>6</mn></mrow></math>, integer <math><mrow><mi>p</mi><mo>≥</mo><mn>6</mn></mrow></math> and integer <math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>}</mo></mrow></mrow></math>, there exists a <math><mi>k</mi></math>-regular homogeneously traceable nonhamiltonian graph of order <math><mrow><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mi>q</mi></mrow></math>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 500-508"},"PeriodicalIF":1.0,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219508","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

Determinantal representations of enumerative polynomials 枚举多项式的行列式表示

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-29 DOI: 10.1016/j.dam.2025.09.025

Shi-Mei Ma , Hong Bian , Jun-Ying Liu , Jean Yeh , Yeong-Nan Yeh

引用次数: 0

On graphs with third largest eccentricity eigenvalue in the interval [−2,−1] 在区间[−2，−1]中具有第三大偏心特征值的图

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-27 DOI: 10.1016/j.dam.2025.09.027

Yuanfen Song , Maurizio Brunetti , Jianfeng Wang

引用次数: 0

Near automorphisms of powers of a path 路径幂的近自同构

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-26 DOI: 10.1016/j.dam.2025.09.015

Shoushuang Chen, Shikun Ou

引用次数: 0

Augmenting a hypergraph to have a matroid-based (f,g)-bounded (α,β)-limited packing of rooted hypertrees 扩充一个超图，使其具有基于矩阵的(f,g)-有界(α,β)-有根超树的有限填充

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-25 DOI: 10.1016/j.dam.2025.09.023

Pierre Hoppenot, Zoltán Szigeti

{"title":"Augmenting a hypergraph to have a matroid-based (f,g)-bounded (α,β)-limited packing of rooted hypertrees","authors":"Pierre Hoppenot, Zoltán Szigeti","doi":"10.1016/j.dam.2025.09.023","DOIUrl":"10.1016/j.dam.2025.09.023","url":null,"abstract":"<div><div>The aim of this paper is to further develop the theory of packing trees in a graph. We first prove the classic result of Nash-Williams (Nash-Williams, 1961) and Tutte (Tutte, 1961) on packing spanning trees by adapting Lovász’ proof (Lovász, 1976) of the seminal result of Edmonds (Edmonds, 1973) on packing spanning arborescences in a digraph. Our main result on graphs extends the theorem of Katoh and Tanigawa (Katoh and Tanigawa, 2013) on matroid-based packing of rooted trees by characterizing the existence of such a packing satisfying the following further conditions: for every vertex <math><mi>v</mi></math>, there are given a lower bound <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> and an upper bound <math><mrow><mi>g</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></math> on the number of trees rooted at <math><mi>v</mi></math> and there are given a lower bound <math><mi>α</mi></math> and an upper bound <math><mi>β</mi></math> on the total number of roots. We also answer the hypergraphic version of the problem. Furthermore, we are able to solve the augmentation version of the latter problem, where the goal is to add a minimum number of edges to have such a packing. The methods developed in this paper to solve these problems may have other applications in the future.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"379 ","pages":"Pages 469-481"},"PeriodicalIF":1.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157969","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

Chorded cycle facets of the clique partitioning polytope 团分割多面体的弦环面

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-24 DOI: 10.1016/j.dam.2025.09.020

Bjoern Andres , Jannik Irmai , Lucas Fabian Naumann

{"title":"Chorded cycle facets of the clique partitioning polytope","authors":"Bjoern Andres , Jannik Irmai , Lucas Fabian Naumann","doi":"10.1016/j.dam.2025.09.020","DOIUrl":"10.1016/j.dam.2025.09.020","url":null,"abstract":"<div><div>The <math><mi>q</mi></math>-chorded <math><mi>k</mi></math>-cycle inequalities are a class of valid inequalities for the clique partitioning polytope. It is known that for <math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>}</mo></mrow></mrow></math>, these inequalities induce facets of the clique partitioning polytope if and only if <math><mi>k</mi></math> is odd. Here, we characterize such facets for arbitrary <math><mi>k</mi></math> and <math><mi>q</mi></math>. More specifically, we prove that the <math><mi>q</mi></math>-chorded <math><mi>k</mi></math>-cycle inequalities induce facets of the clique partitioning polytope if and only if two conditions are satisfied: <math><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow></math> mod <math><mi>q</mi></math>, and if <math><mrow><mi>k</mi><mo>=</mo><mn>3</mn><mi>q</mi><mo>+</mo><mn>1</mn></mrow></math> then <math><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow></math> or <math><mi>q</mi></math> is even. This establishes the existence of many facets induced by <math><mi>q</mi></math>-chorded <math><mi>k</mi></math>-cycle inequalities beyond those previously known.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"378 ","pages":"Pages 662-670"},"PeriodicalIF":1.0,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158057","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

Upper bound of the list r-hued chromatic number 列表r色数的上界

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-24 DOI: 10.1016/j.dam.2025.09.021

Li Liu , Fengxia Liu , Yun Li , Hong-Jian Lai , Hua Cai

引用次数: 0

The d-blocker number and d-transversal number of hexagonal systems 六边形体系的d-阻挡数和d-截数

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-09-24 DOI: 10.1016/j.dam.2025.09.018

Hailun Wu

{"title":"The d-blocker number and d-transversal number of hexagonal systems","authors":"Hailun Wu","doi":"10.1016/j.dam.2025.09.018","DOIUrl":"10.1016/j.dam.2025.09.018","url":null,"abstract":"<div><div>The carbon skeleton of a benzenoid hydrocarbon is often represented by a hexagonal system <math><mi>H</mi></math> with a perfect matching (or Kekulé structure). Vukičević and Trinajstić defined the anti-Kekulé number <math><mrow><mi>a</mi><mi>k</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> as the smallest number of edges of <math><mi>H</mi></math> whose removal results in a connected graph without Kekulé structures. In general, this article investigates related parameters, the <math><mi>d</mi></math>-blocker number <math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> and the <math><mi>d</mi></math>-transversal number <math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>, introduced by Zenklusen et al. These quantify the minimum sizes of an edge subset whose removal reduces the matching number by <math><mi>d</mi></math>, and an edge subset that contains at least <math><mi>d</mi></math> edges of every maximum matching, respectively. For parallelogram, regular hexagon-shaped, and cata-condensed hexagonal systems <math><mi>H</mi></math>, we derive explicit formulas for the <math><mi>d</mi></math>-blocker number <math><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> for all <math><mrow><mn>1</mn><mo>≤</mo><mi>d</mi><mo>≤</mo><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>/</mo><mn>2</mn></mrow></math>, and explicit expressions or bounds for the <math><mi>d</mi></math>-transversal number <math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>. These results extend the robustness analysis of Kekulé structures and generalize the matching preclusion number (corresponding to <math><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></math>) in benzenoid systems.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"380 ","pages":"Pages 175-186"},"PeriodicalIF":1.0,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159809","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