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Acta Mathematica Vietnamica

VERTEXSET CONTAINED IN LONGEST DOMINATING CYCLES IN GRAPHS

icon-email VU DINH HOA

Abstract

Let G be an undirected and simple graph. A cycle C in G is called a {\it dominating cycle} if V(G)V(C) is an independent set of vertices in G. G is called {\it dominable} if G contains a dominating cycle C, and we say G is {\it dominated} by C. In this paper we establish sets of vertices which are contained in any longest dominating cycle in G.