Planar Digraphs without Large Acyclic Sets

被引：3
|
作者：
Knauer, Kolja [1 ]
Valicov, Petru [1 ]
Wenger, Paul S. [2 ]
机构：
[1] Aix Marseille Univ, CNRS, LIF, UMR 7279, F-13288 Marseille, France
[2] Rochester Inst Technol, Sch Math Sci, Rochester, NY 14623 USA
来源：
JOURNAL OF GRAPH THEORY | 2017年 / 85卷 / 01期
关键词：
planar digraphs; acyclic set; feedback vertex set;
D O I：
10.1002/jgt.22061
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a directed graph, an acyclic set is a set of vertices inducing a directed subgraph with no directed cycle. In this note, we show that for all integers ng3, there exist oriented planar graphs of order n and digirth g for which the size of the maximum acyclic set is at most remvoe<n(g-2)+1g-1. When g=3 this result disproves a conjecture of Harutyunyan and shows that a question of Albertson is best possible. (C) 2016 Wiley Periodicals, Inc.
引用
收藏
页码：288 / 291
页数：4
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