Geodesic
An improved inequality related to Vizing's conjecture
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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Vizing conjectured in 1963 that $\gamma(G \Box H) \geq \gamma(G)\gamma(H)$ for any graphs $G$ and $H$. A graph $G$ is said to satisfy Vizing's conjecture if the conjectured inequality holds for $G$ and any graph $H$. Vizing's conjecture has been proved for $\gamma(G) \le 3$, and it is known to hold for other classes of graphs. Clark and Suen in 2000 showed that $\gamma(G \Box H) \geq \frac{1}{2}\gamma(G)\gamma(H)$ for any graphs $G$ and $H$. We give a slight improvement of this inequality by tightening their arguments.
DOI : 10.37236/15
Classification : 05C69, 05C76
Mots-clés : cartesian product 
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     title = {An improved inequality related to {Vizing's} conjecture},
     journal = {The electronic journal of combinatorics},
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     doi = {10.37236/15},
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Stephen Suen; Jennifer Tarr. An improved inequality related to Vizing's conjecture. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/15

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