Abstract
A conjecture of Luo, Tian and Wu (2022) says that for every positive integer k and every finite tree T with bipartition X and Y (denote t=max{|X|,|Y|}), every k-connected bipartite graph G with δ(G)≥k+t contains a subtree T′≅T such that κ(G−V(T′))≥k. In this paper, we confirm this conjecture for caterpillars when k=3 and spiders when k≤3.
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