Validity of the weakened Hadwiger hypothesis
Validity up to complementation in graph theory
Vermutungen über numerierbare Graphen.
Vertex deletion games with parity rules.
Vertex-strength of fuzzy graphs.
Vizing's conjecture and the one-half argument
The domination number of a graph G is the smallest order, γ(G), of a dominating set for G. A conjecture of V. G. Vizing [5] states that for every pair of graphs G and H, γ(G☐H) ≥ γ(G)γ(H), where G☐H denotes the Cartesian product of G and H. We show that if the vertex set of G can be partitioned in a certain way then the above inequality holds for every graph H. The class of graphs G which have this type of partitioning includes those whose 2-packing number is no smaller than γ(G)-1 as well as the...