Strong chromatic index of planar graphs with large girth
نویسندگان
چکیده
منابع مشابه
Strong chromatic index of planar graphs with large girth
Let ∆ ≥ 4 be an integer. In this note, we prove that every planar graph with maximum degree ∆ and girth at least 10∆+46 is strong (2∆−1)-edgecolorable, that is best possible (in terms of number of colors) as soon as G contains two adjacent vertices of degree ∆. This improves [6] when ∆ ≥ 6.
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It was conjectured by Jaeger that 4k-edge connected graphs admit a (2k + 1, k)-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least 4k have circular chromatic number at most 2 + 1 k . Even this restricted version of Jaeger’s conjecture is largely open. The k = 1 case is the well-known Grötzsch 3-colour theorem. This paper ...
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Kostochka, A.V., List edge chromatic number of graphs with large girth, Discrete Mathematics 101 (1992) 189-201. It is shown that the list edge chromatic number of any graph with maximal degree A and girth at least 8A(ln A + 1.1) is equal to A + 1 or to A.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2014
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1763