The Last Fraction of a Fractional Conjecture

Reed conjectured that for every ε > 0 and every integer ∆, there exists g such that the fractional total chromatic number of every graph with maximum degree ∆ and girth at least g is at most ∆ + 1 + ε. The conjecture was proven to be true when ∆ = 3 or ∆ is even. We settle the conjecture by proving it for the remaining cases.

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Frantisek Kardos, Daniel Král', Jean-Sébastien Sereni
• Keywords: Conjecture, Maximum Degree, SIAMDM 2010, Total Chromatic Number