Geodesic
Almost regular partition of a~graph
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part VII, Tome 427 (2014), pp. 105-113

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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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     author = {K. S. Savenkov},
     title = {Almost regular partition of a~graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--113},
     publisher = {mathdoc},
     volume = {427},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_427_a6/}
}
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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/