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- W3014259384 abstract "The notion of weak saturation was introduced by Bollobas in 1968. Let $F$ and $H$ be graphs. A spanning subgraph $G subseteq F$ is weakly $(F,H)$-saturated if it contains no copy of $H$ but there exists an ordering $e_1,ldots,e_t$ of $E(F)setminus E(G)$ such that for each $i in [t]$, the graph $G cup {e_1,ldots,e_i}$ contains a copy $H'$ of $H$ such that $e_i in H'$. Define $wsat(F,H)$ to be the minimum number of edges in a weakly $(F,H)$-saturated graph. In this paper, we prove for all $t ge 2$ and $n ge 3t-3$, that $wsat(K_n,K_{t,t}) = (t-1)(n + 1 - t/2)$, and we determine the value of $wsat(K_n,K_{t-1,t})$ as well. For fixed $2 le s < t$, we also obtain bounds on $wsat(K_n,K_{s,t})$ that are asymptotically tight." @default.
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- W3014259384 date "2020-04-02" @default.
- W3014259384 modified "2023-09-27" @default.
- W3014259384 title "Weak saturation numbers of complete bipartite graphs in the clique" @default.
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