High-Girth Graphs Avoiding a Minor are Nearly Bipartite
نویسندگان
چکیده
Let H be a xed graph. We show that any H-minor free graph of high enough girth has a circular-chromatic number arbitrarily close to two. Equivalently, such graphs have homomorphisms into a large odd circuit. In particular, graphs of high girth and of bounded genus or bounded tree width are \nearly bipartite" in this sense. For example, any planar graph of girth at least 16 admits a homomorphism onto a pentagon. We also obtain tight bounds in a few speci c cases of small forbidden minors.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 83 شماره
صفحات -
تاریخ انتشار 2001