Girth and fractional chromatic number of planar graphs

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Abstract

In 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 we provide upper and lower bounds for this quantity. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 201–217, 2002; DOI 10.1002/jgt10024

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