An Improved Inequality Related to Vizing's Conjecture

Vizing conjectured in 1963 that γ(G2H) > γ(G)γ(H) for any graphs G and H. A graph G is said to satisfy Vizing’s conjecture if the conjectured inequality holds for G and any graph H. Vizing’s conjecture has been proved for γ(G) 6 3, and it is known to hold for other classes of graphs. Clark and Suen in 2000 showed that γ(G2H) > 12γ(G)γ(H) for any graphs G… CONTINUE READING