Geodesic
Domination, packing and excluded minors
The electronic journal of combinatorics, Tome 10 (2003)
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Let $\gamma(G)$ be the domination number of a graph $G$, and let $\alpha_k(G)$ be the maximum number of vertices in $G$, no two of which are at distance $\le k$ in $G$. It is easy to see that $\gamma(G)\ge \alpha_2(G)$. In this note it is proved that $\gamma(G)$ is bounded from above by a linear function in $\alpha_2(G)$ if $G$ has no large complete bipartite graph minors. Extensions to other parameters $\alpha_k(G)$ are also derived.
DOI : 10.37236/1749
Classification : 05C69, 05C83 
@article{10_37236_1749,
     author = {Thomas B\"ohme and Bojan Mohar},
     title = {Domination, packing and excluded minors},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1749},
     zbl = {1024.05066},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1749/}
}
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Thomas Böhme; Bojan Mohar. Domination, packing and excluded minors. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1749

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