A Menger-Type Theorem for Two Induced Paths

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-05-03 DOI:10.1137/23m1573082

Sandra Albrechtsen, Tony Huynh, Raphael W. Jacobs, Paul Knappe, Paul Wollan

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1438-1450, June 2024.
Abstract. We give an approximate Menger-type theorem for the case when a graph [math] contains two [math] paths [math] and [math] such that [math] is an induced subgraph of [math]. More generally, we prove that there exists a function [math], such that for every graph [math] and [math], either there exist two [math] paths [math] and [math] such that the distance between [math] and [math] is at least [math], or there exists [math] such that the ball of radius [math] centered at [math] intersects every [math] path.

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两条诱导路径的门格尔定理

SIAM 离散数学杂志》第 38 卷第 2 期第 1438-1450 页，2024 年 6 月。摘要。当一个图[math]包含两条[math]路径[math]和[math]，且[math]是[math]的诱导子图时，我们给出了一个近似门格尔定理。更广义地说，我们证明存在一个函数[math]，使得对于每一个图[math]和[math]，要么存在两条[math]路径[math]和[math]，使得[math]和[math]之间的距离至少为[math]，要么存在[math]，使得以[math]为中心的半径为[math]的球与每一条[math]路径相交。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.