Abstract.
Let G be a 2-connected graph with maximum degree Δ (G)≥d, and let x and y be distinct vertices of G. Let W be a subset of V(G)−{x, y} with cardinality at most d−1. Suppose that max{d G(u), d G(v)}≥d for every pair of vertices u and v in V(G)−({x, y}∪W) with d G(u,v)=2. Then x and y are connected by a path of length at least d−|W|.
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Received: February 5, 1998 Revised: April 13, 1998
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Hirohata, K. On the Existence of a Long Path Between Specified Vertices in a 2-Connected Graph. Graphs Comb 16, 269–273 (2000). https://doi.org/10.1007/PL00007222
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DOI: https://doi.org/10.1007/PL00007222