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Complete forcing numbers of primitive coronoids

Author

Listed:
  • Shou-Jun Xu

    (Lanzhou University)

  • Xiu-Song Liu

    (Lanzhou University)

  • Wai Hong Chan

    (The Hong Kong Institute of Education)

  • Heping Zhang

    (Lanzhou University)

Abstract

Let $$G$$ G be a graph with edge set $$E(G)$$ E ( G ) that admits a perfect matching $$M$$ M . A forcing set of $$M$$ M is a subset of $$M$$ M contained in no other perfect matching of $$G$$ G . A complete forcing set of $$G$$ G , recently introduced by Xu et al. (J Combin Optim 29(4):803–814, 2015c), is a subset of $$E(G)$$ E ( G ) to which the restriction of any perfect matching is a forcing set of the perfect matching. The minimum possible cardinality of a complete forcing set of $$G$$ G is the complete forcing number of $$G$$ G . Previously, Xu et al. (J Combin Optim 29(4):803–814, 2015c) gave an expression for the complete forcing number of a hexagonal chain and a recurrence relation for complete forcing numbers of catacondensed hexagonal systems. In this article, by the constructive proof, we give an explicit analytical expression for the complete forcing number of a primitive coronoid, a circular single chain consisting of congruent regular hexagons (i.e., Theorem 3.9).

Suggested Citation

  • Shou-Jun Xu & Xiu-Song Liu & Wai Hong Chan & Heping Zhang, 2016. "Complete forcing numbers of primitive coronoids," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 318-330, July.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:1:d:10.1007_s10878-015-9881-y
    DOI: 10.1007/s10878-015-9881-y
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    Cited by:

    1. Xin He & Heping Zhang, 2023. "Complete forcing numbers of complete and almost-complete multipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-20, September.

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