Geodesic
The independence number of dense graphs with large odd girth
The electronic journal of combinatorics, Tome 2 (1995)
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Let $G$ be a graph with $n$ vertices and odd girth $2k+3$. Let the degree of a vertex $v$ of $G$ be $d_1 (v)$. Let $\alpha (G)$ be the independence number of $G$. Then we show $\alpha (G) \geq 2^{-\left({{k-1}\over {k}}\right)} \left[ \displaystyle{\sum_{v\in G}} d_1 (v)^{{{1}\over {k-1}}} \right]^{(k-1)/k}$. This improves and simplifies results proven by Denley.
DOI : 10.37236/1221
Classification : 05C35
Mots-clés : dense graphs, odd girth, independence number 
@article{10_37236_1221,
     author = {James B. Shearer},
     title = {The independence number of dense graphs with large odd girth},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1221},
     zbl = {0811.05032},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1221/}
}
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James B. Shearer. The independence number of dense graphs with large odd girth. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1221

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