An improvement in the two-packing bound related to Vizing's conjecture

Authors

Kimber Wolff, Clayton State UniversityFollow

Abstract

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Wolff, Kimber (2020) "An improvement in the two-packing bound related to Vizing's conjecture," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 5.
DOI: 10.20429/tag.2020.070105
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss1/5