Weak saturation number of a complete bipartite graph

Tongtong Xu and Baoyindureng Wu

Applied Mathematics and Computation, 2023, vol. 455, issue C

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+1Keywords: Clique; Complete bipartite graphs; Weak saturation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002667

DOI: 10.1016/j.amc.2023.128097

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