Discrete Mathematics最新文献

英文中文

Spectral extrema of graphs with fixed size: Forbidden star forests 固定尺寸图的谱极值：禁星森林

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-06 DOI: 10.1016/j.disc.2025.114976

Yanting Zhang , Ligong Wang

The spectral radius of a graph G, denoted by

ρ (G)

, is the largest eigenvalue of its adjacency matrix. The Brualdi-Hoffman-Turán type problem is to determine the maximum spectral radius among all m-edge graphs which do not contain specific forbidden subgraphs. Denote by

S_{ℓ}

the star on

ℓ + 1

vertices. Let F be a star forest, where

F = \cup_{i = 1}^{k} S_{ℓ_{i}}

with

k \geq 2

and

ℓ_{i} \geq 1

for

i \in [k]

. In this paper, we study the Brualdi-Hoffman-Turán type problem for star forests, and prove that if G is an F-free graph with size m, then its spectral radius satisfies

ρ (G) \leq \frac{1}{2} (k - 2 + \sqrt{4 m - k^{2} + 2 k})

, with equality if and only if

G = K_{k - 1} \lor (\frac{m}{k - 1} - \frac{k - 2}{2}) K_{1}

, provided that

m \geq {(2 k - 1)}^{2} {(\sum_{i = 1}^{k} ℓ_{i} + k - 2)}^{2}

图G的谱半径，用ρ(G)表示，是其邻接矩阵的最大特征值。Brualdi-Hoffman-Turán类型问题是确定所有不包含特定禁止子图的m边图的最大谱半径。用S表示在1个顶点上的星号。设F是一个星林，其中对于i∈[k]， F=∪i= 1ks_i，且k≥2且_i≥1。本文研究了星林的Brualdi-Hoffman-Turán型问题，证明了若G是大小为m的无f图，则其谱半径满足ρ(G)≤12(k−2+4m−k2+2k)，且当且仅当G=Kk−1∨(mk−1−k−22)K1，且m≥(2k−1)2(∑i=1k∑i +k−2)2。

引用次数: 0

The Hamilton–Waterloo problem for triangle-factors and Hamiltonian cycles solved 求解了三角因子和哈密顿循环的哈密顿-滑铁卢问题

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-06 DOI: 10.1016/j.disc.2025.114966

Mariusz Meszka

We complete a solution to the Hamilton-Waterloo problem in the case when 2-factors are either triangle-factors or Hamiltonian cycles. Namely, we prove that for each

k \geq 1

and r such that

0 \leq r \leq 3 k + 1

, there exists a 2-factorization of the complete graph

K_{6 k + 3}

in which r of the 2-factors are Hamiltonian cycles and the remaining

(3 k + 1 - r)

2-factors are Δ-factors, except when

k = r = 1

我们完成了2因子为三角因子或哈密顿环的Hamilton-Waterloo问题的一个解。即，我们证明了对于k≥1和r，使得0≤r≤3k+1，存在一个完全图K6k+3的2因子分解，其中2因子中的r为哈密顿环，其余（3k+1 - r） 2因子为Δ-factors，除非k=r=1。

引用次数: 0

Sorting permutations using a pop stack with a bypass 使用带有旁路的弹出堆栈对排列进行排序

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-05 DOI: 10.1016/j.disc.2025.114964

Lapo Cioni , Luca Ferrari , Rebecca Smith

We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never been investigated previously.

In the present paper, we give a characterization of sortable permutations in terms of forbidden patterns and reinterpret the resulting enumerating sequence using a class of restricted Motzkin paths. Moreover, we describe an algorithm to compute the set of all preimages of a given permutation, thanks to which we characterize permutations having a small number of preimages. Finally, we provide a full description of the preimages of principal classes of permutations, and we discuss the device consisting of two pop stacks in parallel, again with a bypass operation.

我们引入了一种新的排列排序装置，它利用了一个带有旁路操作的pop堆栈。这就产生了一个排序机器，它比通常的Popstacksort算法更强大，而且似乎以前从未被研究过。在本文中，我们给出了基于禁止模式的可排序排列的一个表征，并利用一类受限莫兹金路径重新解释了由此产生的枚举序列。此外，我们描述了一种算法来计算给定排列的所有预像的集合，因此我们表征了具有少量预像的排列。最后，我们提供了置换主要类的原象的完整描述，并且我们讨论了由两个并行的pop堆栈组成的设备，同样具有旁路操作。

引用次数: 0

On the size and structure of certain subsequence sum set 某子序列和集的大小和结构

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-05 DOI: 10.1016/j.disc.2025.114975

Jagannath Bhanja

We study the following arithmetic questions regarding subsequence sums: How large is the set of subsequence sums, where each element of this set is a sum of at least s (a fixed number) distinct terms, and what are the sets for which the subsequence sum set minimizes? We prove a near-optimal lower bound for the size of this subsequence sum set over the group of residues modulo an odd prime p. We then establish the optimal lower bound for the size of this subsequence sum set over the group of integers and characterize the optimal sequences that achieve this lower bound.

我们研究了以下关于子序列和的算术问题：子序列和的集合有多大，其中该集合的每个元素是至少s（固定数量）个不同项的和，以及子序列和集合最小的集合是什么？我们证明了这个子序列和集的大小在残数群上模一个奇素数p的近最优下界。然后我们建立了这个子序列和集的大小在整数群上的最优下界，并描述了实现这个下界的最优序列。

引用次数: 0

The Turán number of Berge-linear forests in hypergraphs 超图中berge -线性森林的Turán个数

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-05 DOI: 10.1016/j.disc.2025.114971

Lin-Peng Zhang , Hajo Broersma , Ligong Wang

<div><div>Let <math><mi>F</mi></math> be a family of graphs, and let H be a hypergraph. H is called a Berge-<math><mi>F</mi></math> if for some <math><mi>F</mi><mo>∈</mo><mi>F</mi></math>, there exists an injection <math><mi>θ</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>→</mo><mi>V</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> and a bijection <math><mi>ϕ</mi><mo>:</mo><mi>E</mi><mo>(</mo><mi>F</mi><mo>)</mo><mo>→</mo><mi>E</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> such that <math><mo>{</mo><mi>θ</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>,</mo><mi>θ</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>}</mo><mo>⊆</mo><mi>ϕ</mi><mo>(</mo><mi>e</mi><mo>)</mo></math> for each <math><mi>e</mi><mo>=</mo><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo><mo>∈</mo><mi>E</mi><mo>(</mo><mi>F</mi><mo>)</mo></math>. H is called Berge-<math><mi>F</mi></math>-free if H contains no subhypergraph isomorphic to any Berge-<math><mi>F</mi></math>. The Turán number of a Berge-<math><mi>F</mi></math>, denoted by <math><msub><mrow><mi>ex</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mtext>Berge-</mtext><mi>F</mi><mo>)</mo></math>, is defined as the maximum number of edges in an n-vertex Berge-<math><mi>F</mi></math>-free r-uniform hypergraph. A linear forest is a graph all components of which are paths or isolated vertices. Denote by <math><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub></math> the family of all linear forests containing n vertices and k edges. In this paper, we determine the value of <math><msub><mrow><mi>ex</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mtext>Berge-</mtext><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>)</mo></math> for the cases <math><mn>3</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mo>⌈</mo><mfrac><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo><mo>−</mo><mn>2</mn></math> and <math><mi>r</mi><mo>≥</mo><mi>k</mi><mo>+</mo><mn>1</mn></math>. Furthermore, we characterize the extremal hypergraphs for the cases <math><mn>3</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mfrac><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>3</mn></math> and <math><mi>r</mi><mo>≥</mo><mi>k</mi><mo>+</mo><mn>1</mn></math>, when k is odd, and for the cases <math><mn>3</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mfrac><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></math> and <math><mi>r</mi><mo>≥</mo><mi>k</mi><mo>+</mo><mn>1</mn></math>, when k is even. We establish an upper bound on <math><msub><mrow><mi>ex</mi></mrow><mrow><

设F是一个图族，设H是一个超图。如果对于某些F∈F，存在一个注入θ:V(F)→V(H)和一个双注入φ:E(F)→E(H)，使得对于每个E ={u, V}∈E(F), {θ(u),θ(V)}≥≥φ (E)， H称为Berge-F。如果H不包含与任何Berge-F同构的子超图，则称H为无Berge-F。Berge-F的Turán个数，用exr（n,Berge-F）表示，定义为n顶点无Berge-F的r-均匀超图的最大边数。线性森林是一个图，它的所有组成部分都是路径或孤立的顶点。用Ln k表示所有包含n个顶点和k条边的线性森林族。在本文中,我们确定的价值exr (Berge-Ln n, k)的情况下3 r≤≤⌈k + 12⌉−2 r≥k + 1。进一步刻画了k为奇数时3≤r≤k+12−3和r≥k+1的极值超图，以及k为偶数时3≤r≤k2−2和r≥k+1的极值超图。对于其他几种情况，我们建立了exr（n,Berge-Ln,k）的上界。我们的结果扩展了最近发表的关于Turán berge匹配和线性森林数量的结果。

引用次数: 0

Uniformly sampling random directed hypergraphs with fixed degrees 固定度随机有向超图的均匀抽样

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-05 DOI: 10.1016/j.disc.2025.114961

Yanna J. Kraakman, Clara Stegehuis

Many complex systems show non-pairwise interactions, which can be captured by hypergraphs. In this work, we propose an edge-swapping method to sample random directed hypergraphs with fixed vertex and hyperarc degrees, which can be applied to different classes of directed hypergraphs (containing self-loops, degenerate hyperarcs and/or multi-hyperarcs). We prove that this method indeed samples uniformly from the classes with self-loops and multi-hyperarcs, and that the method may not sample uniformly from classes without self-loops, or with self-loops and degenerate hyperarcs but without multi-hyperarcs. We present a partial result on the class with self-loops, but without degenerate hyperarcs or multi-hyperarcs.

许多复杂系统表现出非成对相互作用，这可以通过超图来捕获。在这项工作中，我们提出了一种边交换方法来采样具有固定顶点和超弧度的随机有向超图，该方法可以应用于不同类别的有向超图（包含自环，退化超弧和/或多超弧）。我们证明了该方法确实能从具有自环和多超弧的类中均匀采样，而该方法不能从没有自环的类中均匀采样，也不能从具有自环和退化超弧但没有多超弧的类中均匀采样。我们给出了有自循环但没有退化超弧或多超弧的类的部分结果。

引用次数: 0

Revisiting d-distance (independent) domination in trees and in bipartite graphs 回顾树和二部图中的d距离（独立）支配

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-05 DOI: 10.1016/j.disc.2025.114972

Csilla Bujtás , Vesna Iršič Chenoweth , Sandi Klavžar , Gang Zhang

The d-distance p-packing domination number

γ_{d}^{p} (G)

of G is the minimum size of a set of vertices of G which is both a d-distance dominating set and a p-packing. In 1994, Beineke and Henning conjectured that if

d \geq 1

and T is a tree of order

n \geq d + 1

, then

γ_{d}^{1} (T) \leq \frac{n}{d + 1}

. They supported the conjecture by proving it for

d \in {1, 2, 3}

. In this paper, it is proved that

γ_{d}^{1} (G) \leq \frac{n}{d + 1}

holds for any bipartite graph G of order

n \geq d + 1

, and any

d \geq 1

. Trees T for which

γ_{d}^{1} (T) = \frac{n}{d + 1}

holds are characterized. It is also proved that if T has ℓ leaves, then

γ_{d}^{1} (T) \leq \frac{n - ℓ}{d}

(provided that

n - ℓ \geq d

), and

γ_{d}^{1} (T) \leq \frac{n + ℓ}{d + 2}

(provided that

n \geq d

). The latter result extends Favaron's theorem from 1992 asserting that

γ_{1}^{1} (T) \leq \frac{n + ℓ}{3}

. In both cases, trees that attain the equality are characterized and relevant conclusions for the d-distance domination number of trees derived.

G的d距离p-填料支配数γdp(G)是G的一个顶点集的最小大小，该顶点集既是d距离支配集又是p-填料。1994年，Beineke和Henning推测，如果d≥1且T是n阶≥d+1的树，则γd1(T)≤nd+1。他们通过证明d∈{1,2,3}来支持这个猜想。本文证明了γd1(G)≤nd+1对任意阶n≥d+1的二部图G和任意d≥1成立。对γd1(T)=nd+1成立的树T进行表征。还证明了如果T有r个叶，则γd1(T)≤n−r d（假设n−r≥d）， γd1(T)≤n+ r d+2（假设n≥d）。后一个结果推广了1992年的Favaron定理，断言γ11(T)≤n+ l3。在这两种情况下，都对达到相等的树进行了表征，并得出了树的d距离支配数的相关结论。

引用次数: 0

Extremal graphs for disjoint union of vertex-critical graphs 顶点临界图不相交并的极值图

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-02 DOI: 10.1016/j.disc.2025.114973

Wenqian Zhang

For a graph F, let

EX (n, F)

be the set of F-free graphs of order n with the maximum number of edges. The graph F is called vertex-critical, if the deletion of its some vertex induces a graph with smaller chromatic number. For example, an odd wheel (obtained by connecting a vertex to a cycle of even length) is a vertex-critical graph with chromatic number 3.

For

h \geq 2

, let

F_{1}, F_{2}, . . ., F_{h}

be vertex-critical graphs with the same chromatic number. Let

\cup_{1 \leq i \leq h} F_{i}

be the disjoint union of them. In this paper, we characterize the graphs in

EX (n, \cup_{1 \leq i \leq h} F_{i})

, when there is a proper order among the graphs

F_{1}, F_{2}, . . ., F_{h}

. This solves a conjecture (on extremal problem for disjoint union of odd wheels) proposed by Xiao and Zamora [16].

对于图F，设EX（n，F）为边数最大的n阶无F图的集合。如果图F的某些顶点被删除，则图F的色数变小，则称为顶点临界图。例如，奇轮（通过将一个顶点连接到一个偶数长度的循环得到）是一个色数为3的顶点临界图。当h≥2时，设F1，F2，…， h是具有相同色数的顶点临界图。设∪1≤i≤hFi是它们的不相交并。在本文中，当图F1，F2，…，Fh之间存在适当的序时，我们刻画了EX（n,∪1≤i≤hFi）中的图。这解决了Xiao和Zamora[16]提出的一个猜想（关于奇轮不接合并的极值问题）。

引用次数: 0

The nucleus of the Hamming graph H(D,q) 汉明图的核H（D,q）

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-02 DOI: 10.1016/j.disc.2025.114969

Jun Hu , Gengsheng Zhang , Bo Hou

The concept of the nucleus of a distance-regular graph was recently introduced by P. Terwilliger. Let Γ be a Q-polynomial distance-regular graph with vertex set Y. Let

T = T (x)

be the Terwilliger algebra of Γ with respect to a fixed vertex

x \in Y

. Then the nucleus of Γ with respect to x is a certain T-module. In this paper, we describe the nucleus of the Hamming graph

H (D, q)

and construct two bases for the nucleus by using the Hamming semilattice

H (D, q + 1)

. Our main result partially answers an open problem proposed by P. Terwilliger (2025) [21].

距离正则图核的概念是最近由P. Terwilliger提出的。设Γ为一个顶点集为Y的q多项式距离正则图，设T=T(x)为Γ关于一个固定顶点x∈Y的Terwilliger代数。那么Γ的原子核相对于x是一个t模。本文描述了Hamming图H（D,q）的核，并利用Hamming半格H（D,q+1）构造了核的两个基。我们的主要结果部分回答了P. Terwilliger（2025）提出的一个开放性问题。

引用次数: 0

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2026-01-01

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Discrete Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀