Abstract
A greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empty. We have recently shown that any greedy clique decomposition of a graph of ordern has at mostn 2/4 cliques. A greedy max-clique decomposition is a particular kind cf greedy clique decomposition where maximum cliques are removed, instead of just maximal ones. In this paper, we show that any greedy max-clique decompositionC of a graph of ordern has
, wheren(C) is the number of vertices inC.
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McGuinness, S. Greedy maximum-clique decompositions. Combinatorica 14, 335–343 (1994). https://doi.org/10.1007/BF01212981
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DOI: https://doi.org/10.1007/BF01212981