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2008

Fractional coloring and the odd Hadwiger's conjecture

8 years 10 months ago
Fractional coloring and the odd Hadwiger's conjecture
Gerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience, 1995], page 115) conjectured that if a graph has no odd complete minor of order p, then it is (p - 1)-colorable. This is an analogue of the well known conjecture of Hadwiger, and in fact, this would immediately imply Hadwiger's conjecture. The current best known bound for the chromatic number of graphs without an odd complete minor of order p is O(p log p) by the recent result by Geelen et al. [J. Geelen, B. Gerards, B. Reed, P. Seymour, A. Vetta, On the odd variant of Hadwiger's conjecture (submitted for publication)], and by Kawarabayashi [K. Kawarabayashi, Note on coloring graphs without odd Kk-minors (submitted for publication)] (but later). But, it seems very hard to improve this bound since this would also improve the current best known bound for the chromatic number of graphs without a complete minor of order p. Motivated by this problem, we prove that the "fractional chr...
Ken-ichi Kawarabayashi, Bruce A. Reed
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where EJC
Authors Ken-ichi Kawarabayashi, Bruce A. Reed
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