An application of Vizing and Vizing-like adjacency lemmas to Vizing’s Independence Number Conjecture of edge chromatic critical graphs

In 1968, Vizing conjectured that, if GG is a ΔΔ-critical graph with nn vertices, then α(G)≤n2, where α(G)α(G) is the independence number of GG. In this note, we apply Vizing and Vizing-like adjacency lemmas to this problem and obtain better bounds for Δ∈{7,…,19}Δ∈{7,…,19}.