Discrete Applied Mathematics最新文献

英文中文

Weighted cages 加权的笼子里

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1016/j.dam.2025.12.047

G. Araujo-Pardo , C. De la Cruz , M. Matamala , M.A. Pizaña

Cages (

r

-regular graphs of girth

g

and minimum order) and their variants have been studied for over seventy years. Here we propose a new variant, weighted cages. We characterize their existence; for cases

g = 3, 4

we determine their order; we give Moore-like bounds and present some computational results.

笼形图（周长g和最小阶的r-正则图）及其变体已经被研究了70多年。在这里，我们提出一种新的变体，加权笼。我们描述它们的存在；对于情况g=3,4，我们确定它们的顺序；给出了类摩尔边界，并给出了一些计算结果。

引用次数: 0

Robust optimization of multi-skill resource-constrained project networks considering staff fatigue under uncertainty 考虑不确定性下员工疲劳的多技能资源约束项目网络鲁棒优化

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1016/j.dam.2025.12.071

Zihan Ning , Ran Ma , Zhengwen He , Xiaoyan Zhang

In project implementation, uncertainty factors have significant impacts. How to effectively safeguard staff working conditions while ensuring timely project delivery under uncertain environments has emerged as a critical issue urgently requiring resolution in the project management domain. The Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP), as a typical combinatorial optimization challenge, provides theoretical foundations for addressing the issues. This problem can be abstracted as a complex multi-layer network graph optimization model. This study focuses on robust project scheduling under multi-skill resource constraints, aiming to generate proactive optimization schedules that simultaneously minimize staff maximum fatigue accumulation and maximize robustness. To accurately reflect realistic execution environments, this research incorporates activity uncertainty into staff fatigue levels considerations within the model construction, thereby better characterizing the actual impact of uncertain factors on staff fatigue levels. In terms of algorithmic design, this paper introduces priority selection strategies during the schedule generation process to enhance solution quality, and develops an Improved Non-dominated Sorting Genetic Algorithm II (INSGA-II) featuring dual-mode adaptive selection mechanisms and diversity-driven elite retention adjustments. Experimental results demonstrate that through multi-metric comparisons, the proposed comprehensive algorithm significantly outperforms traditional methods. Furthermore, this study conducts in-depth experimental analysis and interpretation regarding solution robustness and the improved fatigue function, validating the effectiveness and practicality of the proposed methodology.

在项目实施过程中，不确定性因素对项目的影响是显著的。如何在不确定的环境下有效保障员工的工作条件，同时保证项目的及时交付，已成为项目管理领域亟待解决的关键问题。多技能资源约束项目调度问题（MS-RCPSP）作为典型的组合优化问题，为解决这一问题提供了理论基础。该问题可以抽象为一个复杂的多层网络图优化模型。本研究关注多技能资源约束下的鲁棒项目调度，旨在生成同时最小化人员最大疲劳积累和最大化鲁棒性的主动优化调度。为了准确反映现实的执行环境，本研究在模型构建中将活动的不确定性纳入到员工疲劳水平的考虑中，从而更好地表征不确定性因素对员工疲劳水平的实际影响。在算法设计方面，本文在调度生成过程中引入优先级选择策略以提高求解质量，并开发了一种具有双模式自适应选择机制和多样性驱动的精英保留调整的改进非支配排序遗传算法II （INSGA-II）。实验结果表明，通过多指标比较，本文提出的综合算法明显优于传统方法。此外，本文还对解的鲁棒性和改进的疲劳函数进行了深入的实验分析和解释，验证了所提出方法的有效性和实用性。

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引用次数: 0

A note on robber locating game 关于抢劫犯定位游戏的说明

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1016/j.dam.2025.12.061

Rahul Das, Ushnish Sarkar

The robber locating game on a simple connected graph is a variant of pursuit evasion game where a cop wants to locate a mobile, invisible and omniscient robber hiding in the vertices of the graph using distance queries. This game has two versions depending on whether the robber is allowed to backtrack or not. The minimum numbers of rounds required to locate the robber, against any strategy he adopts, in the two versions of the game are referred to as backtrack and non-backtrack location numbers of the graph respectively. However, if the robber is immobile, then the minimum numbers of rounds required to locate the invisible robber is called the sequential metric dimension of the graph. This article gives a lower bound of the backtrack and non-backtrack location numbers in terms of the metric dimension and diameter. This has been done by establishing a lower bound of the sequential metric dimension. A hideout is a subgraph

G

of a graph

H

such that the mobile, invisible and omniscient robber can win by remaining on the vertices of

G

. We prove sufficient conditions for a graph to be a hideout for both backtracking and non-backtracking scenarios.

简单连通图上的抢劫犯定位游戏是追捕逃避游戏的一种变体，其中警察希望利用距离查询来定位隐藏在图顶点中的移动的、不可见的、无所不知的抢劫犯。这个游戏有两个版本，取决于强盗是否被允许返回。在两个版本的博弈中，针对抢劫者采取的任何策略，定位抢劫者所需的最小回合数分别称为图的回溯和非回溯位置数。然而，如果抢劫者是固定不动的，那么定位看不见的抢劫者所需的最小回合数称为图的顺序度量维度。本文根据公制尺寸和直径给出了回溯和非回溯位置数的下界。这是通过建立顺序度量维度的下界来实现的。藏身处是图H的子图G，使得移动的、不可见的、无所不知的强盗可以通过留在G的顶点上而获胜。我们证明了图在回溯和非回溯两种情况下都是藏身处的充分条件。

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引用次数: 0

Aspects of a randomly growing cluster in Rd,d≥2 随机生长的聚类在Rd，d≥2的方面

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1016/j.dam.2025.12.062

Alan Frieze , Ravi Kannan , Wesley Pegden

We consider a simple model of a growing cluster of points in

R^{d}, d \geq 2

. Beginning with a point

X_{1}

located at the origin, we generate a random sequence of points

X_{1}, X_{2}, \dots, X_{i}, \dots,

. To generate

X_{i}, i \geq 2

we choose a uniform integer

j

[i - 1] = (1, 2, \dots, i - 1)

and then let

X_{i} = X_{j} + D_{i}

where

D_{i} = (δ_{1}, \dots, δ_{d})

. Here the

δ_{j}

are independent copies of the Normal distribution

N (0, σ_{i})

, where

σ_{i} = i^{- α}

for some

α > 0

. We prove that for any

α > 0

the resulting point set is bounded a.s., and moreover, that the points generated look like samples from a

β

-dimensional subset of

R^{d}

from the standpoint of the minimum lengths of combinatorial structures on the point-sets, where

β = min (d, 1 / α)

我们考虑一个简单的模型，在Rd，d≥2点的增长簇。从原点的点X1开始，我们生成点X1，X2，…，Xi，…，的随机序列。为了生成Xi，i≥2，我们在[i−1]=1,2，…，i−1中选择一个均匀整数j，然后令Xi=Xj+Di，其中Di=（δ1，…，δd）。这里的δj是正态分布N（0,σi）的独立副本，其中σi=i - α，对于某些α>；0。我们证明了对于任意α>；0生成的点集是有界的，并且从点集上组合结构的最小长度的角度来看，生成的点看起来像来自Rd的β维子集的样本，其中β=min（d,1/α）。

引用次数: 0

On 2-distance (2Δ+6)-coloring of planar graphs 平面图形的2-距离（2Δ+6）着色

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.063

Jiahao Yu, Min Chen

Given a graph

G = (V, E)

, a 2-distance

k

-coloring is a mapping

π : V (G) \to {1, 2, \dots, k}

such that any two vertices within distance at most two receive distinct colors. A graph admitting such a coloring is called 2-distance. It is known that every planar graph is 2-distance

(2 Δ + 16)

-colorable if the maximum degree

Δ \geq 8

(Song and Lai, 2018) and 2-distance

(2 Δ + 7)

-colorable if

Δ \geq 9

(Bousquet et al., 2023). In this paper, we strengthen these bounds by proving that every planar graph with

Δ \geq 8

is 2-distance

(2 Δ + 6)

-colorable, thereby advancing progress toward Wegner’s conjecture.

给定一个图G=(V，E)，一个2-distance k-coloring是一个映射π:V(G)→{1,2，…，k}，使得距离不超过两个的任意两个顶点得到不同的颜色。允许这种着色的图称为2-距离。已知，如果最大度Δ≥8 (Song and Lai, 2018)，则每个平面图为2-distance （2Δ+16）可色(2-distance （2Δ+7）可色（Δ≥9）（Bousquet et al., 2023）。在本文中，我们通过证明Δ≥8的每个平面图都是2-距离（2Δ+6）可色来加强这些界限，从而推进了Wegner猜想的进展。

引用次数: 0

Construction, extension and paths of near-homogeneous tournaments 构建、扩展和路径近乎同质化的比赛

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.059

Rongxia Tang , Zhaojun Chen , Zan-Bo Zhang

A homogeneous tournament is a tournament with

4 t + 3

vertices such that every arc is contained in exactly

t + 1

cycles of length 3. Homogeneous tournaments are the first class of tournaments that are proved to be path extendable, which means that every nonhamiltonian path

P

in such a tournament

T

can be extended to a path

P^{'}

with the same initial and terminal vertex and

V (P^{'}) = V (P) \cup {u}

for a certain vertex

u \in V (T) ∖ V (P)

. In order to find more path extendable tournaments we study the generalization of homogeneous tournaments called near-homogeneous tournaments, in which every arc is contained in

t

t + 1

cycles of length 3. Near-homogeneity has been defined in tournaments with

4 t + 1

vertices. In this paper, we raise a new method to construct near-homogeneous tournaments with

4 t + 1

vertices. We then show that the definition of near-homogeneous tournament can be extended to tournaments with an even number of vertices. Finally we verify path extendability of near-homogeneous tournaments, thus expand the class of path extendable tournaments.

齐次比赛是指有4t+3个顶点的比赛，这样每个弧都包含在长度为3的t+1个循环中。齐次竞赛是第一类被证明是路径可扩展的竞赛，这意味着在这样一个竞赛T中的每一个非哈密顿路径P都可以被扩展到具有相同初始顶点和终点顶点的路径P '，并且对于某个顶点u∈V(T)∈V(P)∈V(P)∈V(P)≠V(P)∪{u}。为了找到更多路径可扩展的比赛，我们研究了齐次比赛的推广，称为近齐次比赛，其中每个弧都包含在t或t+1个长度为3的循环中。近同质性在4t+1个顶点的比赛中被定义。本文提出了一种构造具有4t+1个顶点的近齐次竞赛的新方法。然后，我们证明了近齐次比赛的定义可以扩展到具有偶数个顶点的比赛。最后，我们验证了近似同构竞赛的路径可扩展性，从而扩展了路径可扩展性竞赛的类别。

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引用次数: 0

Extremal distance spectra of graphs and essential connectivity 图的极值距离谱和基本连通性

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.070

Daoxia Zhang, Dan Li, Wenxiu Ding

A graph is trivial if it contains only one vertex. The essential connectivity of

G

, denoted by

κ^{'} (G)

, is the minimum number of vertices of

G

whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the

n

-vertex graph of given essential connectivity with minimum distance spectral radius. We also characterize the extremal graphs attaining the minimum distance spectral radius among all connected graphs with fixed essential connectivity and minimum degree. Furthermore, we characterize the extremal digraphs with minimum distance spectral radius among the strongly connected digraphs with given essential connectivity.

如果一个图只包含一个顶点，那么它是平凡的。G的基本连通性，用κ ' (G)表示，是G的最小顶点数，其移除会产生至少有两个非平凡分量的断开图。在本文中，我们确定了具有最小距离谱半径的给定基本连通的n顶点图。我们还描述了在所有具有固定基本连通性和最小度的连通图中获得最小距离谱半径的极值图。进一步，我们刻画了具有给定基本连通性的强连通有向图中具有最小距离谱半径的极值有向图。

引用次数: 0

Maximizing the number of maximal independent sets in graphs with a given matching number 具有给定匹配数的图中最大独立集的数量最大化

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.057

Xiaotong Gu, Hongzhi Deng, Yuting Tian, Jianhua Tu

In this paper, we determine the maximum number of maximal independent sets for three families of graphs. The first family comprises all 2-connected graphs with matching number

t

. The second family consists of all unicyclic graphs with matching number

t

. The third family encompasses all graphs on

n

vertices with matching number

t

where

2 t \leq n \leq 3 t

; note that the case

n \geq 3 t

has been settled in previous work.

在本文中，我们确定了三种图族的最大独立集的最大数目。第一族包含匹配数为t的所有2连通图，第二族包含匹配数为t的所有单环图，第三族包含匹配数为t的n个顶点上的所有图，其中2t≤n≤3t；注意，前面的工作已经解决了n≥3t的情况。

引用次数: 0

Forbidden configurations and dominating bicliques in undirected 2-quasi best match graphs 无向2-拟最优匹配图中的禁止构型和支配双链

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2026.01.001

Annachiara Korchmaros , Peter F. Stadler

2-quasi best match graphs (2qBMGs) are directed graphs that capture a notion of close relatedness in phylogenetics. Here, we investigate the underlying undirected graph of a 2qBMG (un2qBMG) and show that it contains neither a path

P_{l}

nor a cycle

C_{l}

of length

l \geq 6

as an induced subgraph. This property guarantees the existence of specific vertex decompositions with dominating bicliques that provide further insights into their structure.

2-准最佳匹配图（2qbmg）是有向图，它捕获了系统发育中近亲关系的概念。本文研究了一个2qBMG （un2qBMG）的底层无向图，证明了它既不包含路径Pl，也不包含长度为l≥6的循环Cl作为诱导子图。这个性质保证了特定顶点分解的存在，这些顶点分解具有主导曲线，可以进一步了解它们的结构。

引用次数: 0

Even cycle decompositions of the line graphs of cubic graphs 三次图的线形图的连循环分解

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.052

Chuixiang Zhou, Yuxi Zou

An even cycle decomposition of a graph is defined as a partition of its edges into cycles of even length. Let

G

be a 2-connected cubic graph. Markström conjectured that the line graph

L (G)

G

admits an even cycle decomposition. Suppose that

F = C_{1} \cup C_{2} \cup \dots \cup C_{k}

is a 2-factor of

G

, where each

C_{i}

(

1 \leq i \leq k

) is a cycle. Let

G_{F}

be the graph obtained from

G

by contracting each

C_{i}

(

1 \leq i \leq k

) to a vertex and deleting the resulting loops and parallel edges. In this paper, we prove that Markström’s conjecture is true if

G_{F}

is isomorphic to a tree for some 2-factor

F

G

图的偶环分解被定义为将图的边划分为偶数长度的环。设G是一个二连通三次图。Markström推测G的线形图L(G)允许偶循环分解。设F=C1∪C2∪⋯∪Ck是G的一个2因子，其中每个Ci（1≤i≤k）是一个循环。设GF为由G将每个Ci（1≤i≤k）缩并到一个顶点，并删除由此产生的环路和平行边得到的图。本文证明了如果GF同构于某2因子F (G)的树，则Markström的猜想是成立的。

引用次数: 0

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Discrete Applied Mathematics

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