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Distance-restricted matching extendability of fullerene graphs

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Abstract

A fullerene graph is a 3-connected cubic plane graph whose all faces are bounded by 5- or 6-cycles. In this paper, we show that a matching M of a fullerene graph can be extended to a perfect matching if the following hold: (i) three faces around each vertex in \(\{x,y:xy\in M\}\) are bounded by 6-cycles and (ii) the edges in M lie at distance at least 13 pairwise.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 26800086 (to M.F), JSPS KAKENHI Grant Number JP16K17646 (to S.T) and research grant of Senshu University (to S.T).

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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. Department of Civil and Environmental Engineering, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima, 731-5193, Japan

    Masanori Takatou

  3. School of Network and Information, Senshu University, 2-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa, 214-8580, Japan

    Shoichi Tsuchiya

Authors
  1. Michitaka Furuya
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  2. Masanori Takatou
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  3. Shoichi Tsuchiya
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Correspondence to Shoichi Tsuchiya.

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Furuya, M., Takatou, M. & Tsuchiya, S. Distance-restricted matching extendability of fullerene graphs. J Math Chem 56, 606–617 (2018). https://doi.org/10.1007/s10910-017-0806-0

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  • DOI: https://doi.org/10.1007/s10910-017-0806-0

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