The size of edge chromatic critical graphs with maximum degree 6



In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117–134; Russian Math Surveys 23 (1968), 125–142] conjectured that for any edge chromatic critical graph equation image with maximum degree equation image, equation image. This conjecture has been verified for equation image. In this article, by applying the discharging method, we prove the conjecture for equation image. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 149–171, 2009