Geodesic
Vizing's conjecture for graphs with domination number 3 -- a new proof
Boštjan Brešar1
1University of Maribor, Faculty of Natural Sciences and Mathematics
The electronic journal of combinatorics, Tome 22 (2015) no. 3

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Zbl
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 $H$, $\gamma(G\Box H) \ge 3\gamma(H)$.
DOI : 10.37236/5182
Classification : 05C69, 05C76
Mots-clés : Cartesian product, domination, Vizing's conjecture

Boštjan Brešar  1

1 University of Maribor, Faculty of Natural Sciences and Mathematics 
Boštjan Brešar. Vizing's conjecture for graphs with domination number 3 -- a new proof. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5182
@article{10_37236_5182,
     author = {Bo\v{s}tjan Bre\v{s}ar},
     title = {Vizing's conjecture for graphs with domination number 3 -- a new proof},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {3},
     doi = {10.37236/5182},
     zbl = {1323.05099},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5182/}
}
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