Vizing's Conjecture for Graphs with Domination Number 3 - a New Proof
Copyright policy )Vizing's Conjecture for Graphs with Domination Number 3 - a New Proof
Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this note we use a new, transparent approach to prove Vizing's conjecture for graphs with domination number 3; that is, we prove that for any graph $G$ with $\gamma(G)=3$ and an arbitrary graph $H$, $\gamma(G\Box H) \ge 3\gamma(H)$.
- University of Maribor Slovenia
Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Graph operations (line graphs, products, etc.), Cartesian product, Vizing's conjecture, domination
Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Graph operations (line graphs, products, etc.), Cartesian product, Vizing's conjecture, domination
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