Abstract
Let G be a balanced bipartite graph with bipartite sets X, Y. We say that G is Hamilton-biconnected if there is a Hamilton path connecting any vertex in X and any vertex in Y. We define the bipartite independent number \(\alpha ^o_B(G)\) to be the maximum integer \(\alpha \) such that for any integer partition \(\alpha =s+t\), G has an independent set formed by s vertices in X and t vertices in Y. In this paper we show that if \(\alpha ^o_B(G)\le \delta (G)\) then G is Hamilton-biconnected, unless G has a special construction.
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Li, B. Bipartite Independent Number and Hamilton-Biconnectedness of Bipartite Graphs. Graphs and Combinatorics 36, 1639–1653 (2020). https://doi.org/10.1007/s00373-020-02211-7
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DOI: https://doi.org/10.1007/s00373-020-02211-7