Tight Bound on Treedepth in Terms of Pathwidth and Longest Path

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2023-12-19 DOI:10.1007/s00493-023-00077-w

引用次数: 0

Abstract

We show that every graph with pathwidth strictly less than a that contains no path on \(2^b\) vertices as a subgraph has treedepth at most 10ab. The bound is best possible up to a constant factor.

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用路径宽度和最长路径严格约束树丛深度

摘要我们证明，每一个路径宽度严格小于 a 的图，如果不包含 \(2^b\) 个顶点上的路径作为子图，那么它的树深度最多为 10ab。这个界限是在一个常数因子以内的最佳值。

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

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.