The decycling number of cubic graphs

Authors:
Narong Punnim
Affiliations:
Department of Mathematics, Srinakharinwirot University, Bangkok, Thailand
Venue:
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
Year:
2003

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Abstract

For a graph G, a subset S ⊆ V(G), is said to be a decycling set of G if if G ∖ S is acyclic. The cardinality of smallest decycling set of G is called the decycling number of G and it is denoted by φ(G). Bau and Beineke posed the following problems: Which cubic graphs G with | G | = 2n satisfy $\phi(G)=\lceil{\frac{n+1}{2}}\rceil$? In this paper, we give an answer to this problem.