Powers of paths in tournaments

IF 0.9 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Combinatorics, Probability & Computing Pub Date : 2020-10-12 DOI:10.1017/S0963548321000067

N. Dragani'c, Franccois Dross, J. Fox, António Girão, F. Havet, D'aniel Kor'andi, W. Lochet, David Munh'a Correia, A. Scott, B. Sudakov

引用次数: 5

Abstract

In this short note we prove that every tournament contains the k-th power of a directed path of linear length. This improves upon recent results of Yuster and of Girão. We also give a complete solution for this problem when k=2, showing that there is always a square of a directed path of length , which is best possible.

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比赛中路径的力量

在这篇简短的笔记中，我们证明了每个比武包含线性长度的有向路径的k次幂。这与Yuster和gir最近的研究结果相比有所改善。当k=2时，我们也给出了这个问题的完全解，表明总有一个长度为有向路径的平方，这是最好的可能。

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

Combinatorics, Probability & Computing 数学-计算机：理论方法

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.

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