Geodesic
Spectral saturation: inverting the spectral Turán theorem
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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Let $\mu\left( G\right) $ be the largest eigenvalue of a graph $G$ and $T_{r}\left( n\right) $ be the $r$-partite Turán graph of order $n.$We prove that if $G$ is a graph of order $n$ with $\mu\left( G\right)>\mu\left( T_{r}\left( n\right) \right)$, then $G$ contains various large supergraphs of the complete graph of order $r+1,$ e.g., the complete $r$-partite graph with all parts of size $\log n$ with an edge added to the first part.We also give corresponding stability results.
DOI : 10.37236/122
Classification : 05C35, 05C50
Mots-clés : r-partite Turan graph, complete r-partite graph, stability results 
@article{10_37236_122,
     author = {Vladimir Nikiforov},
     title = {Spectral saturation: inverting the spectral {Tur\'an} theorem},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/122},
     zbl = {1159.05031},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/122/}
}
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Vladimir Nikiforov. Spectral saturation: inverting the spectral Turán theorem. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/122

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