@MISC{Mcguinness94greedyclique, author = {Sean Mcguinness}, title = {Greedy Clique Decompositions and the Turán Numbers}, year = {1994} }

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Abstract

. In this paper, we show that for p 4 if C is a clique decomposition obtained by removing maximal cliques(ie. their edges) of order at least p one by one until none remain, in which case the remaining edges are removed one by one, then the sum of the orders of the cliques in C is at most 2t p\Gamma1 (n): Here t p\Gamma1 (n) denotes the number of edges in the Tur'an graph of order n which has no cliques of order p: 1. Introduction All graphs in this paper will be assumed to be simple; that is, without loops or multiple edges. For a graph G, we let V (G) denote its vertex set and E(G) denote its edge set. The cardinalities of V (G) and E(G) will be denoted by n(G) and m(G), respectively. By a clique we shall mean a complete subgraph and by a clique decomposition, we shall mean a collection of cliques which partition the edge set of the graph. A greedy clique decomposition of a graph is a pair (C; OE) consisting of a clique decomposition C and a total ordering OE on C where C is obta...