Discrete Applied Mathematics最新文献

英文中文

Maximum bond incident degree indices for trees and unicyclic graphs with given maximum degree 给定最大度的树和单环图的最大键关联度指标

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-12 DOI: 10.1016/j.dam.2025.12.021

Ioan Tomescu

The bond incident degree (BID) index

T_{f} (G)

of a connected graph

G

with edge-weight function

f (x, y)

is defined as

T_{f} (G) = \sum_{v_{i} v_{j} \in E (G)} f (d (v_{i}), d (v_{j})),

where

f (x, y) > 0

is a symmetric real function with

x \geq 1

and

y \geq 1

and

d (u)

is the degree of vertex

u

G

. In this paper, we find extremal trees and unicyclic graphs of order

n

with given maximum degree having maximum bond incident degree index

T_{f}

if edge-weight symmetric function

f (x, y)

satisfies five conditions. These conditions are fulfilled by sum-connectivity index, general sum-connectivity index, modified Sombor index and harmonic index.

定义具有边权函数f（x,y）的连通图G的键关联度（BID）指标Tf(G)为Tf(G)=∑vivj∈E(G)f(d(vi),d(vj))，其中f(x,y)>；0为x≥1，y≥1的对称实函数，d(u)为G中顶点u的度。本文在边权对称函数f（x,y）满足5个条件的情况下，得到具有最大键关联度的n阶极值树和单环图。这些条件由和连通性指数、一般和连通性指数、修正Sombor指数和调和指数来满足。

引用次数: 0

Complexity of action path finding with small precondition sets 小前提条件下动作寻径的复杂性

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-12 DOI: 10.1016/j.dam.2025.12.009

Peter Damaschke , Karinne Ramirez-Amaro

Suppose that we are given a finite set of Boolean attributes and a set of actions defined on them. Every action has the effect of changing some attribute values and may also depend on further attribute values which are, however, not changed. The subset of attributes affected by an action is known as precondition. The goal is to find some sequence of executable actions that transform a given initial state into a desired target state. This type of problem appears, e.g., in robot motion planning. In this paper, we study cases of the problem where the precondition of every action only depends on a conjunction of terms with at most two attributes. We classify a number of cases as polynomial-time solvable or NP-complete. They amount to extended versions of some classic graph problems, among them topological orderings and perfect matchings. This appears to be the first systematic study of preconditions, despite the rich literature on many aspects of path finding in finite state spaces. A complete dichotomy of polynomial-time and NP-complete cases remains an open question.

假设给定一组有限的布尔属性和一组定义在这些属性上的动作。每个操作都会改变一些属性值，并且还可能依赖于未改变的其他属性值。受操作影响的属性子集称为先决条件。目标是找到将给定的初始状态转换为期望的目标状态的一些可执行动作序列。这种类型的问题出现，例如，在机器人运动规划。本文研究了每个动作的前提条件只依赖于最多两个属性项的合项的问题。我们将一些情况分类为多项式时间可解或np完全。它们相当于一些经典图问题的扩展版本，其中包括拓扑排序和完美匹配。这似乎是对前提条件的第一个系统研究，尽管在有限状态空间的寻路的许多方面有丰富的文献。多项式时间和np完全情况的完全二分法仍然是一个悬而未决的问题。

引用次数: 0

Several bounds on the spectral radius of uniform hypergraphs 均匀超图谱半径的几个界

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-12 DOI: 10.1016/j.dam.2025.12.014

Chunli Deng , Junchen Dong , Haifeng Li

For

k

-uniform hypergraphs, this paper establishes several new bounds on the spectral radii of the adjacency and signless Laplacian tensors. These bounds are expressed by vertex degrees and average 2-degrees of hypergraphs. Furthermore, the bounds are compared with the known results, and the example shows that our bounds are better in some cases. As applications, the spectral radii of the generalized power hypergraphs of stars and cycles are presented, respectively.

对于k-一致超图，本文在邻接张量和无符号张量的谱半径上建立了几个新的界。这些边界由顶点度和超图的平均2度表示。此外，将边界与已知结果进行了比较，实例表明我们的边界在某些情况下更好。作为应用，分别给出了恒星和周期的广义幂超图的谱半径。

引用次数: 0

Spectral condition for k-factor-criticality in t-connected graphs t连通图中k因子临界的谱条件

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-12 DOI: 10.1016/j.dam.2025.12.019

Tingyan Ma , Edwin R. van Dam , Ligong Wang

A graph

G

is called

k

-factor-critical if

G - S

has a perfect matching for every

S \subseteq V (G)

with

| S | = k

. A connected graph

G

is called

t

-connected if it has more than

t

vertices and remains connected whenever fewer than

t

vertices are removed. We give a condition on the number of edges and a condition on the spectral radius for

k

-factor-criticality in

t

-connected graphs.

如果G−S对每一个S的|S的|=k有完全匹配，则称图G为k因子临界。连通图G被称为t连通图，如果它有超过t个顶点，并且在移除少于t个顶点时保持连通。给出了t连通图中k因子临界的边数和谱半径的一个条件。

引用次数: 0

Colorful two-piercing theorem for boxes 盒子的彩色双穿孔定理

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-12 DOI: 10.1016/j.dam.2025.11.044

Sourav Chakraborty , Arijit Ghosh , Soumi Nandi

We prove a colorful extension of a Helly-type theorem by Danzer and Grünbaum (1982) concerning two-piercing families of axis-parallel boxes in

R^{d}

. We also show that our result is tight by constructing extremal families that achieve the bound. Related work includes a graph-theoretic proof of the original theorem by Pendavingh et al. (2008), and a two-piercing result for lower-dimensional boxes by Baños and Oliveros (2018).

我们证明了Danzer和gr nbaum（1982）关于Rd中轴平行盒的两个穿孔族的helly型定理的一个彩色推广。我们还通过构造达到界的极值族证明了我们的结果是紧密的。相关工作包括Pendavingh等人（2008）对原始定理的图论证明，以及Baños和Oliveros（2018）对低维盒子的双穿孔结果。

引用次数: 0

The robust selection problem with information discovery 信息发现的鲁棒选择问题

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-11 DOI: 10.1016/j.dam.2025.12.012

Xiaoyu Chen , Marc Goerigk , Michael Poss

We explore a multiple-stage variant of the min–max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this information, one can then choose the set of items to be selected, still facing uncertainty on the unobserved parameters. In this paper, we study two specific variants of this problem. The first variant considers objective uncertainty and focuses on selecting a single item. The second variant considers constraint uncertainty instead, which means that some selected items may fail. We show that both problems are NP-hard in general. We also propose polynomial-time algorithms for special cases where the sets of items that can be simultaneously queried are defined by a cardinality or a knapsack constraint. For the problem with constraint uncertainty, we also show how the objective function can be expressed as a linear program, leading to a mixed-integer linear programming reformulation for the general case. We illustrate the performance of this formulation using numerical experiments.

我们探索了包含查询的预算不确定性的最小-最大鲁棒选择问题的多阶段变体。首先，查询项目子集并获得其不确定参数的确切值。有了这些信息，人们就可以选择要选择的一组项目，但仍然面临着未观察到的参数的不确定性。本文研究了这一问题的两个具体变体。第一种变体考虑客观不确定性，侧重于选择单个项目。第二种变体考虑约束不确定性，这意味着某些选择的项目可能会失败。我们证明这两个问题一般都是np困难的。我们还提出了多项式时间算法，用于特殊情况，其中可以同时查询的项目集由基数或背包约束定义。对于具有约束不确定性的问题，我们还展示了如何将目标函数表示为线性规划，从而得到一般情况下的混合整数线性规划的重新表述。我们用数值实验来说明这个公式的性能。

引用次数: 0

On cross-2-intersecting families 在交叉的2相交的族上

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-10 DOI: 10.1016/j.dam.2025.12.002

Yanhong Chen , Anshui Li , Biao Wu , Huajun Zhang

Two families

A \subseteq (\frac{[n]}{k})

and

B \subseteq (\frac{[n]}{ℓ})

are called cross-

t

-intersecting if

| A \cap B | \geq t

for all

A \in A

B \in B

. Let

n

k

and

ℓ

be positive integers such that

n \geq 3.38 ℓ

and

ℓ \geq k \geq 2

. In this paper, we will determine the upper bound of

| A | | B |

for cross-2-intersecting families

A \subseteq (\frac{[n]}{k})

and

B \subseteq (\frac{[n]}{ℓ})

. The structures of the extremal families attaining the upper bound are also characterized. The similar result obtained by Tokushige can be considered as a special case of ours when

k = ℓ

, but under a more strong condition

n > 3.42 k

. Moreover, combined with the results obtained in this paper, the complicated extremal structures attaining the upper bound for nontrivial cases can be relatively easy to reach with similar techniques.

对于所有A∈A， B∈B，如果|A∩B|≥t，则称A和B两个族为正交交集。设n， k， r为正整数，使n≥3.38,r≥k≥2。本文拟确定正交2相交的A、B两种族的|、|、|、|的上界。对达到上界的极族结构也进行了表征。Tokushige得到的类似结果可以看作是我们在k= r时的特例，但在更强的条件n>；3.42k下。此外，结合本文的结果，对于非平凡情况的上界的复杂极值结构，可以用类似的技术相对容易地达到。

引用次数: 0

The chromatic index of hypergraphs with no intersecting multiple 2-edges 没有多个2边相交的超图的色指数

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-10 DOI: 10.1016/j.dam.2025.12.004

Zhimin Wang , Guiying Yan , Xia Zhang

Shannon’s theorem states that every graph

G

has chromatic index no more than

⌊ \frac{3}{2} Δ (G) ⌋

. In 2000, Dvořák generalized Shannon’s result to hypergraphs without multiple 2-edges, and conjectured every hypergraph

H

has

χ^{'} (H) \leq ⌊ \frac{3}{2} Δ (H) ⌋

, where

Δ (H) = max {\sum_{e ∋ v} (| e | - 1) : v \in V (H)}

. In this paper, we show that the conjecture holds for hypergraphs with no intersecting multiple 2-edges, which extends the result of Dvořák.

香农定理指出每个图G的色指数不大于⌊32Δ(G)⌋。2000年，Dvořák将香农的结果推广到没有多条2边的超图，并推测每个超图H都有χ′(H)≤⌊32Δ(H)⌋，其中Δ(H)=max{∑e↑↑v(|e|−1):v∈v(H)}。在本文中，我们证明了该猜想在没有多条2边相交的超图中成立，推广了Dvořák的结果。

引用次数: 0

Optimal welfare strategies vs Nash Equilibrium strategies in a game with homogeneous players 同质博弈中的最优福利策略与纳什均衡策略

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-10 DOI: 10.1016/j.dam.2025.12.005

Patricia Zu’rob, Abdelrahim S. Mousa

We introduce a welfare–Nash game model for a group of homogeneous players. We characterize player’s behavior based on well-defined quasi-linear utility and establish a unified analytical structure that jointly characterizes welfare optimal strategies and Nash equilibrium strategies. We derive two coalition thresholds, two Nash thresholds, and a general form of welfare thresholds. We give full characterization for the order of all coalition, Nash and welfare thresholds based on the values of the influence parameter of externality. We identify the precise conditions under which players’ behaviors transition between cooperative (welfare-oriented) and selfish (Nash-oriented) regimes. This shows the existence of single, double and degenerate bifurcations between coalition and Nash thresholds. We determine all possible strategies that form optimal welfare strategies or Nash Equilibrium strategies, or neither one nor the other. Finally, we show two phase dynamics in the players’ decision process, and we show how small perturbation on the influence parameter would imply a different dynamical phase to adapt an alternative decision.

我们引入了一组同质参与者的福利纳什博弈模型。我们基于定义良好的准线性效用来表征参与者的行为，并建立了一个统一的分析结构，共同表征福利最优策略和纳什均衡策略。我们推导了两个联盟阈值、两个纳什阈值和福利阈值的一般形式。我们根据外部性影响参数的值，给出了所有联盟、纳什和福利阈值的顺序的充分表征。我们确定了玩家行为在合作（福利导向）和自私（纳什导向）机制之间转换的精确条件。这证明了联盟与纳什阈值之间存在单双分岔和简并分岔。我们决定所有可能形成最优福利策略或纳什均衡策略的策略，或者两者都不选择。最后，我们展示了参与者决策过程中的两个阶段动态，并展示了影响参数的小扰动如何意味着不同的动态阶段来适应备选决策。

{"title":"Optimal welfare strategies vs Nash Equilibrium strategies in a game with homogeneous players","authors":"Patricia Zu’rob, Abdelrahim S. Mousa","doi":"10.1016/j.dam.2025.12.005","DOIUrl":"10.1016/j.dam.2025.12.005","url":null,"abstract":"<div><div>We introduce a welfare–Nash game model for a group of homogeneous players. We characterize player’s behavior based on well-defined quasi-linear utility and establish a unified analytical structure that jointly characterizes welfare optimal strategies and Nash equilibrium strategies. We derive two coalition thresholds, two Nash thresholds, and a general form of welfare thresholds. We give full characterization for the order of all coalition, Nash and welfare thresholds based on the values of the influence parameter of externality. We identify the precise conditions under which players’ behaviors transition between cooperative (welfare-oriented) and selfish (Nash-oriented) regimes. This shows the existence of single, double and degenerate bifurcations between coalition and Nash thresholds. We determine all possible strategies that form optimal welfare strategies or Nash Equilibrium strategies, or neither one nor the other. Finally, we show two phase dynamics in the players’ decision process, and we show how small perturbation on the influence parameter would imply a different dynamical phase to adapt an alternative decision.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"382 ","pages":"Pages 245-258"},"PeriodicalIF":1.0,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737330","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

Star-critical Ramsey numbers of trees versus wheels 恒星临界拉姆齐数树对车轮

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.dam.2025.12.006

Aofei Hu , Yan Li , Yusheng Li , Ye Wang

<div><div>Ramsey theory has significant applications in interconnection networks, such as the identification of structured subgraphs and the analysis of network connectivity. For graphs <math><mi>F</mi></math>, <math><mi>G</mi></math> and <math><mi>H</mi></math>, let <math><mrow><mi>F</mi><mo>→</mo><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> signify that any red/blue edge coloring of <math><mi>F</mi></math> contains a red <math><mi>G</mi></math> or a blue <math><mi>H</mi></math>. The Ramsey number <math><mrow><mi>r</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> is the smallest <math><mi>r</mi></math> such that <math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>→</mo><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>, and the star-critical Ramsey number <math><mrow><msub><mrow><mi>r</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> is the smallest <math><mi>n</mi></math> such that <math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⊔</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>n</mi></mrow></msub><mo>→</mo><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math>, where <math><mrow><mi>r</mi><mo>=</mo><mi>r</mi><mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></mrow></mrow></math> and <math><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>⊔</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>n</mi></mrow></msub></mrow></math> is the graph obtained from <math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msub></math> and an additional vertex <math><mi>v</mi></math> by joining <math><mi>v</mi></math> to <math><mi>n</mi></math> vertices of <math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msub></math> for <math><mrow><mi>n</mi><mo>≤</mo><mi>r</mi><mo>−</mo><mn>1</mn></mrow></math>. In this note, we show that <math><mrow><msub><mrow><mi>r</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>m</mi></mrow></msub><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mi>s</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>+</mo><mn>1</mn></mrow></math> if <math><mi>m</mi></math> is odd and <math><mrow><mi>n</mi><mo>≥</mo><mn>25</mn><mi>m</mi></mrow></math>, and <math><mrow><msub><mrow><mi

拉姆齐理论在互连网络中有着重要的应用，如结构子图的识别和网络连通性的分析。对于图F， G和H，设F→（G，H）表示F的任何红/蓝边染色包含一个红G或一个蓝H。拉姆齐数r（G，H）是最小的r，使得Kr→（G，H）；临界拉姆齐数r * （G，H）是最小的n，使得Kr−1 (r) =r（G，H）和Kr−1 (r) * (K1,n)是由Kr−1和一个附加顶点v组成的图，当n≤r−1时，将v连接到Kr−1的n个顶点。本文证明了r∗(Tn,Ws,m)=(s+1)(n−1)+1，如果m是奇数且n≥25m， r∗(Tn,Ws,m)=s(n−1)+1，如果m是偶数，n≥25（m−1）且s≥4n−1，r∗(Tn,Ws,m)=s(n−1)+1，其中Tn是n阶树，Ws,m =Ks+Cm是广义轮。

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 Applied 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.

﹀