# Union of Cliques in an Undirected Graph

Is it true that any undirected graph is a union of maximal cliques? Since an edge is a size 2 clique?

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It seems obvious for finite graphs. I think that cliques satisfy Zorn's lemme, so in particular, every edge is in a maximal clique in the infinite case, too. – Thomas Andrews Jan 11 '13 at 23:33