Graphs and Combinatorics

, Volume 35, Issue 6, pp 1401–1404 | Cite as

An Improved Bound in Vizing’s Conjecture

  • Shira ZerbibEmail author
Original Paper


A well-known conjecture of Vizing (Vyčisl Sistemy 9:30–43, 1963) is that \(\gamma (G \square H) \ge \gamma (G)\gamma (H)\) for any pair of graphs GH, where \(\gamma \) is the domination number and \(G \square H\) is the Cartesian product of G and H. Suen and Tarr [7], improving a result of Clark and Suen [5], showed \(\gamma (G \square H) \ge \frac{1}{2}\gamma (G)\gamma (H) + \frac{1}{2}\min (\gamma (G),\gamma (H))\). We further improve their result by showing \(\gamma (G \square H) \ge \frac{1}{2}\gamma (G)\gamma (H) + \frac{1}{2}\max (\gamma (G),\gamma (H))\).


Vizing’s conjecture Cartesian product Graph domination 



The author is grateful to Ron Aharoni for helpful discussions.


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsIowa State UniversityAmesUSA

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