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Complete forcing numbers of catacondensed hexagonal systems

Author

Listed:
  • Shou-Jun Xu

    (Lanzhou University)

  • Heping Zhang

    (Lanzhou University)

  • Jinzhuan Cai

    (Hainan University)

Abstract

Let G be a graph with edge set E(G) that admits a perfect matching M. A forcing set of M is a subset of M contained in no other perfect matchings of G. A global forcing set of $$G$$ G , introduced by Vukičević et al., is a subset of $$E(G)$$ E ( G ) on which there are distinct restrictions of any two different perfect matchings of $$G$$ G . Combining the above “forcing” and “global” ideas, we introduce and define a complete forcing set of G as a subset of $$E(G)$$ E ( G ) on which the restriction of any perfect matching $$M$$ M of $$G$$ G is a forcing set of $$M$$ M . The minimum cardinality of complete forcing sets is the complete forcing number of $$G$$ G . First we establish some initial results about these two novel concepts, including a criterion for a complete forcing set, and comparisons between the complete forcing number and global forcing number. Then we give an explicit formula for the complete forcing number of a hexagonal chain. Finally a recurrence relation for the complete forcing number of a catacondensed hexagonal system is derived.

Suggested Citation

  • Shou-Jun Xu & Heping Zhang & Jinzhuan Cai, 2015. "Complete forcing numbers of catacondensed hexagonal systems," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 803-814, May.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9624-x
    DOI: 10.1007/s10878-013-9624-x
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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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