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List 2-distance (Δ + 1)-coloring of planar graphs with girth at least 7

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Abstract

The trivial lower bound for the 2-distance chromatic number χ 2(G) of a graph G with maximum degree Δ is Δ + 1. There are available some examples of the graphs with girth g ≤ 6 that have arbitrarily large Δ and χ 2(G) ≥ Δ + 2. In the paper we improve the known restrictions on Δ and g under which a planar graph G has χ 2(G) = Δ + 1.

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Authors and Affiliations

  1. Institute of Mathematics, Yakutsk State University, ul. Belinskogo 58, Yakutsk, 677891, Russia

    A. O. Ivanova

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  1. A. O. Ivanova
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Correspondence to A. O. Ivanova.

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Original Russian Text © A.O. Ivanova, 2010, published in Diskretnyi Analiz i Issledovanie Operatsii, 2010, Vol. 17, No. 5, pp. 22–36.

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Ivanova, A.O. List 2-distance (Δ + 1)-coloring of planar graphs with girth at least 7. J. Appl. Ind. Math. 5, 221–230 (2011). https://doi.org/10.1134/S1990478911020098

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