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The decycling number of outerplanar graphs

Author

Listed:
  • Huilan Chang

    (National Chiao Tung University
    National University of Kaohsiung)

  • Hung-Lin Fu

    (National Chiao Tung University)

  • Min-Yun Lien

    (National Chiao Tung University)

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.

Suggested Citation

  • Huilan Chang & Hung-Lin Fu & Min-Yun Lien, 2013. "The decycling number of outerplanar graphs," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 536-542, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-012-9455-1
    DOI: 10.1007/s10878-012-9455-1
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