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Long Paths in Bipartite Graphs and Path-Bistar Bipartite Ramsey Numbers

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Abstract

In this paper, we focus on a so-called Fan-type condition assuring us the existence of long paths in bipartite graphs. As a consequence of our main result, we completely determine the bipartite Ramsey numbers \(b(P_{s},B_{t_{1},t_{2}})\), where \(B_{t_{1},t_{2}}\) is the graph obtained from a \(t_{1}\)-star and a \(t_{2}\)-star by joining their centers.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant number 18K13449 (to M.F).

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Authors and Affiliations

  1. College of Liberal Arts and Sciences, Kitasato University, 1-15-1 Kitasato, Minami-ku, Sagamihara, Kanagawa, 252-0373, Japan

    Michitaka Furuya

  2. Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, 240-8501, Japan

    Shun-ichi Maezawa

  3. Faculty of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, 240-8501, Japan

    Kenta Ozeki

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  1. Michitaka Furuya
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  2. Shun-ichi Maezawa
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  3. Kenta Ozeki
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Correspondence to Michitaka Furuya.

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Furuya, M., Maezawa, Si. & Ozeki, K. Long Paths in Bipartite Graphs and Path-Bistar Bipartite Ramsey Numbers. Graphs and Combinatorics 36, 167–176 (2020). https://doi.org/10.1007/s00373-019-02127-x

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  • DOI: https://doi.org/10.1007/s00373-019-02127-x

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