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An Improvement In The Two-Packing Bound Related To Vizing's Conjecture, Kimber Wolff
An Improvement In The Two-Packing Bound Related To Vizing's Conjecture, Kimber Wolff
Theory and Applications of Graphs
Vizing's conjecture states that the domination number of the Cartesian product of graphs is at least the product of the domination numbers of the two factor graphs. In this note we improve the recent bound of Breŝar by applying a technique of Zerbib to show that for any graphs G and H, γ(G x H)≥ γ (G) 2/3(γ(H)-ρ(H)+1), where γ is the domination number, ρ is the 2-packing number, and x is the Cartesian product.