论[数学]最短路径可覆盖的图

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-10 DOI:10.1137/23m1564511

Maël Dumas, Florent Foucaud, Anthony Perez, Ioan Todinca

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引用次数: 0

摘要

SIAM 离散数学杂志》第 38 卷第 2 期第 1840-1862 页，2024 年 6 月。摘要。我们证明，如果一个无向图[math]的边或顶点可以被[math]最短路径覆盖，那么[math]的路径宽度是由[math]的单指数函数上界的。作为推论，我们证明带终端的等距路径覆盖问题（给定一个图[math]和一组称为终端的[math]对顶点，问[math]是否能被[math]最短路径覆盖，每条路径连接一对终端）是关于终端数的 FPT 问题。类似的问题 "有终端的强大地集"（给定一个图[math]和一组[math]终端，问是否存在覆盖[math]的[math]最短路径，每条路径连接一对不同的终端）也是如此。此外，这意味着相关问题等距路径覆盖和强大地集（定义类似，但终点集不是输入的一部分）在参数[math]方面是XP的。

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On Graphs Coverable by [math] Shortest Paths

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1840-1862, June 2024.
Abstract. We show that if the edges or vertices of an undirected graph [math] can be covered by [math] shortest paths, then the pathwidth of [math] is upper-bounded by a single-exponential function of [math]. As a corollary, we prove that the problem Isometric Path Cover with Terminals (which, given a graph [math] and a set of [math] pairs of vertices called terminals, asks whether [math] can be covered by [math] shortest paths, each joining a pair of terminals) is FPT with respect to the number of terminals. The same holds for the similar problem Strong Geodetic Set with Terminals (which, given a graph [math] and a set of [math] terminals, asks whether there exist [math] shortest paths covering [math], each joining a distinct pair of terminals). Moreover, this implies that the related problems Isometric Path Cover and Strong Geodetic Set (defined similarly but where the set of terminals is not part of the input) are in XP with respect to parameter [math].

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.