Geodesic
Almost regular partition of a graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 105-113 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $k\le8$ be a positive integer and $G$ be a graph on $n$ vertices such that each vertex degree of $G$ is at least $\frac{k-1}kn$. It is proved in the paper that the vertex set of $G$ can be partitioned into several cliques of size at most $k$, such that for each positive integer $k_0 there is at most one clique of size $k_0$ in this partition. 
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K. S. Savenkov. Almost regular partition of a graph. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 105-113. http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a6/

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