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

页码：288 / 291

页数：4

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