An improved constant for Vizing's conjecture · arXivDesk2607.01109Jul 1, 2026Algebraic mistake
An improved constant for Vizing's conjecture
Mohsen Aliabadi, Elliot Krop
Abstract
For any graph G=(V,E), a subset S⊆V dominates G if N[S]=V
. The minimum cardinality over all such
is called the domination number, written
. The classical conjecture of V.G. Vizing states that
γ(G□H)≥γ(G)γ(H) where
stands for the Cartesian product of graphs. In this paper, we apply well-known results to prove the Vizing-type inequality
γ(G□H)≥.5809γ(G)γ(H) .