摘要

A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p >= 5, every planar graph of girth p without cycles of length from p + 1 to p(p - 2) is C-p-colorable (that is, it admits a homomorphism to the odd cycle C-p). The assumption of p >= 5 being prime number is necessary, and this conjecture implies a special case of Jaeger's Conjecture that every planar graph of girth 2p - 2 is C-p-colorable for prime p >= 5. In this paper, combining our previous results, we show the fractional coloring version of this conjecture is true. Particularly, the p = 5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.

  • 单位
    南开大学

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