Domination in partitioned graphs with minimum degree two

被引：2

作者：

Henning, Michael A. ^{[1
]}

Vestergaard, Preben Dahl

机构：

[1] Univ KwaZulu Natal, Sch Math Sci, ZA-3209 Pietermaritzburg, South Africa

[2] Univ Aalborg, Dept Math, DK-9220 Aalborg, Denmark

来源：

DISCRETE MATHEMATICS | 2007年 / 307卷 / 9-10期

关键词：

domination; minimum degree two; partitioned graphs; 3-subdivision;

D O I：

10.1016/j.disc.2006.07.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let V-1, V-2 be a partition of the vertex set in a. graph G. For i = 1, 2, let gamma(i) denote the least number of vertices needed in G to dominate V-i. It is known that if G has order n and minimum degree two, then gamma(1) + gamma(2) <= 2n/3. In this paper, we characterize those graphs of order n which are edge-minimal with respect to satisfying the conditions of connected, minimum degree at least two, and gamma(1) + gamma(2) = 2n/3. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：1115 / 1135

页数：21

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