<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1766" altimg="si161.svg"><mml:mi>r</mml:mi></mml:math>-hued <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1771" altimg="si16.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-coloring of planar graphs with girth at least 8 for <mml:math xmlns:mml="http://www.…
نویسندگان
چکیده
Let r,k?1 be two integers. An r-hued k-coloring of the vertices a graph G=(V,E) is proper vertices, such that, for every vertex v?V, number colors in its neighborhood at least min{dG(v),r}, where dG(v) degree v. We prove existence an (r+1)-coloring planar graphs with girth 8 r?9. As corollary, maximum ??9 and admits 2-distance (?+1)-coloring.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2021
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2020.103219