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Bipartite Independent Number and Hamilton-Biconnectedness of Bipartite Graphs

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Abstract

Let G be a balanced bipartite graph with bipartite sets XY. 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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Correspondence to Binlong Li.

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Supported by NSFC (11601429) and the Fundamental Research Funds for the Central Universities (3102019ghjd003).

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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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