Locating Pairs of Vertices on a Hamiltonian Cycle in Bigraphs |
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| Authors: | Ralph J Faudree Jeno Lehel Kiyoshi Yoshimoto |
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| Institution: | 1.The University of Memphis,Memphis,USA;2.Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences,Budapest,Hungary;3.Nihon University,Tokyo,Japan |
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| Abstract: | Let G be a simple \(m\times m\) bipartite graph with minimum degree \(\delta (G)\ge m/2+1\). We prove that for every pair of vertices x, y, there is a Hamiltonian cycle in G such that the distance between x and y along that cycle equals k, where \(2\le k<m/6\) is an integer having appropriate parity. We conjecture that this is also true up to \(k\le m\). |
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