On the Independence Number of Edge Chromatic Critical Graphs

In 1968, Vizing conjectured that for any edge chromatic critical graph G = (V, E) with maximum degree Delta and independence number alpha(G), alpha(G) <= vertical bar V vertical bar/2. This conjecture is still open. In this paper, we prove that alpha(G) <= 3 Delta-2/5 Delta-2 vertical bar V vertical bar for Delta = 11,12 and alpha(G) <= 11 Delta-30/17 Delta-30 vertical bar V vertical bar for 13 <= Delta <= 29. This improves the known bounds for Delta is an element of {11, 12, ..., 29}.