Connecting face hitting sets in planar graphs

被引：5
|
作者：
Schweitzer, Pascal [1 ]
Schweitzer, Patrick [2 ]
机构：
[1] Max Planck Inst Comp Sci, D-66123 Saarbrucken, Germany
[2] Univ Luxembourg, Interdisciplinary Ctr Secur Reliabil & Trust, L-1359 Luxembourg, Luxembourg
来源：
INFORMATION PROCESSING LETTERS | 2010年 / 111卷 / 01期
关键词：
Combinatorial problems; Planar graph; Face hitting set;
D O I：
10.1016/j.ipl.2010.10.008
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n - 6. Furthermore we show that this bound is tight by providing a lower bound in the form of a family of graphs. This improves the previously known upper and lower bound of 11n - 18 and 3n respectively by Grigoriev and Sitters. Our proof is valid for simple graphs with loops and generalizes to graphs embedded in surfaces of arbitrary genus. (c) 2010 Elsevier B.V. All rights reserved.
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页码：11 / 15
页数：5
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