%0 Journal Article %J Ars Combinatoria %D 2011 %T Decompositions of graphs into a given clique-extension %A Sousa, Teresa %P 465–472 %U http://www.combinatorialmath.ca/arscombinatoria/vol100.html %V 100 %X

For r≥3, a clique-extension of order r+1 is a connected graph that consists of a Kr plus another vertex adjacent to at most r-1 vertices of Kr. In this paper we consider the problem of finding the smallest number t such that any graph G of order n admits a decomposition into edge disjoint copies of a fixed graph H and single edges with at most t elements. Here we solve the case when H is a fixed clique-extension of order r+1, for all r≥3 and will also obtain all extremal graphs. This work extends results proved by Bollobás [Math.\ Proc.\ Cambridge Philosophical Soc 79 (1976) 19--24] for cliques.

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