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Weak saturation number of a complete bipartite graph

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  • Xu, Tongtong
  • Wu, Baoyindureng

Abstract

For two graphs H and F, a spanning subgraph G of H is weakly(H,F)-saturated if there is no subgraph isomorphic to F in G, but there is an ordering of the elements in E(H)∖E(G) so that they can be added one at a time, and each addition of an element yields a subgraph F′ isomorphic to F. The weak saturation number wsat(H,F) of F with respect to H is the minimum size of a weakly (H,F)-saturated graph. For any two integers r≥3 and a≥1, we give upper bounds for wsat(Kn,rKa,a) and wsat(Kn,rKa,a+1) respectively. In addition, an upper bound of wsat(Kn,Ka,b) is established for integers n,a,b satisfying a+1

Suggested Citation

  • Xu, Tongtong & Wu, Baoyindureng, 2023. "Weak saturation number of a complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    • Handle: RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002667
    DOI: 10.1016/j.amc.2023.128097
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    References listed on IDEAS

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    1. Song, Feifei & Zhou, Jianjie, 2021. "The partite saturation number of spider," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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