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Distance Constraints on Short Cycles for 3-Colorability of Planar graphs

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Abstract

Montassier et al. showed that every planar graph without cycles of length at most five at distance less than four is 3-colorable [A relaxation of of Havel’s 3-color problem, Inform. Process. Lett. 107 (2008) 107–109]. Borodin, Montassier and Raspaud asked in [Planar graphs without adjacent cycles of length at most seven are 3-colorable, Discrete Math. 310 (2010) 167–173]: is every planar graph without adjacent cycles of length at most five 3-colorable? In this note, we show that every planar graph without cycles of length at most five at distance less than two is 3-colorable.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, China

    Yingli Kang & Yingqian Wang

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  1. Yingli Kang
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  2. Yingqian Wang
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Correspondence to Yingqian Wang.

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Supported by NSFC No. 11271335.

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Kang, Y., Wang, Y. Distance Constraints on Short Cycles for 3-Colorability of Planar graphs. Graphs and Combinatorics 31, 1497–1505 (2015). https://doi.org/10.1007/s00373-014-1476-3

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  • DOI: https://doi.org/10.1007/s00373-014-1476-3

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