The decycling number of outerplanar graphs

Huilan Chang (), Hung-Lin Fu and Min-Yun Lien
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Huilan Chang: National Chiao Tung University
Hung-Lin Fu: National Chiao Tung University
Min-Yun Lien: National Chiao Tung University

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 5, 536-542

Abstract: Abstract For a graph G, let τ(G) be the decycling number of G and c(G) be the number of vertex-disjoint cycles of G. It has been proved that c(G)≤τ(G)≤2c(G) for an outerplanar graph G. An outerplanar graph G is called lower-extremal if τ(G)=c(G) and upper-extremal if τ(G)=2c(G). In this paper, we provide a necessary and sufficient condition for an outerplanar graph being upper-extremal. On the other hand, we find a class $\mathcal{S}$ of outerplanar graphs none of which is lower-extremal and show that if G has no subdivision of S for all $S\in \mathcal{S}$ , then G is lower-extremal.

Keywords: Decycling number; Feedback vertex number; Cycle packing number; Outerplanar graph (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-012-9455-1

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