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 G is a Δ -critical graph with n vertices, then α ( G ) ≤ n 2 , where α ( G ) is the independence number of G . In this note, we apply Vizing and Vizing-like adjacency lemmas to this problem and obtain better bounds for Δ ∈ { 7 , … , 19 } .