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Girth and fractional chromatic number of planar graphs
Journal of Graph Theory, 2002AbstractIn 1959, even before the Four‐Color Theorem was proved, Grötzsch showed that planar graphs with girth at least 4 have chromatic number at the most 3. We examine the fractional analogue of this theorem and its generalizations. For any fixed girth, we ask for the largest possible fractional chromatic number of a planar graph with that girth, and ...
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Fractional chromatic number and circular chromatic number for distance graphs with large clique size
Journal of Graph Theory, 2004AbstractAn Erratum has been published for this article in Journal of Graph Theory 48: 329–330, 2005.Let M be a set of positive integers. The distance graph generated by M, denoted by G(Z, M), has the set Z of all integers as the vertex set, and edges ij whenever |i−j| ∈ M. We investigate the fractional chromatic number and the circular chromatic number
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