Every 4-Colorable Graph With Maximum Degree 4 Has an Equitable 4-Coloring
نویسندگان
چکیده
Chen, Lih, and Wu conjectured that for r ≥ 3, the only connected graphs with maximum degree at most r that are not equitably r-colorable are Kr,r (for odd r) and Kr+1. If true, this would be a joint strengthening of the Hajnal-Szemerédi Theorem and Brooks' Theorem. Chen, Lih, and Wu proved that their conjecture holds for r = 3. In this paper we study properties of the hypothetical minimum counter-examples to this conjecture and the structure of optimal colorings of such graphs. Using these properties and structure, we show that the Chen Lih Wu Conjecture holds for r ≤ 4. Mathematics Subject Classi cation: 05C15, 05C35.
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عنوان ژورنال:
- Journal of Graph Theory
دوره 71 شماره
صفحات -
تاریخ انتشار 2012