Elsevier

Discrete Mathematics

Volume 310, Issue 5, 6 March 2010, Pages 1050-1058
Discrete Mathematics

Degree conditions for group connectivity

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Abstract

Let G be a 2-edge-connected simple graph on n13 vertices and A an (additive) abelian group with |A|4. In this paper, we prove that if for every uvE(G), max{d(u),d(v)}n/4, then either G is A-connected or G can be reduced to one of K2,3,C4 and C5 by repeatedly contracting proper A-connected subgraphs, where Ck is a cycle of length k. We also show that the bound n13 is the best possible.

Keywords

Abelian group
A-connected
Group connectivity

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