Author:
Chen Kevin,Karson Sean,Liu Dan,Shen Jian
Abstract
For a simple digraph G without directed triangles or digons, let \beta(G) be the size of the smallest subset X of E(G) such that G\X has no directed cycles, and let \gamma(G) be the number of unordered pairs of nonadjacent vertices in G. In 2008, Chudnovsky, Seymour, and Sullivan showed that \beta(G) \leq \gamma(G) and conjectured that \beta(G) \leq \gamma(G)/2. Recently, Dunkum, Hamburger, and Por proved that \beta(G)\leq .88\gamma(G). In this note, we prove that \beta(G) \leq .8616 \gamma(G).
Publisher
University of Wyoming Libraries
Subject
Algebra and Number Theory
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Packing arc-disjoint cycles in oriented graphs;Journal of Computer and System Sciences;2024-08
2. 3-Free Strong Digraphs with the Maximum Size;Graphs and Combinatorics;2021-07-25