Krausz dimension and its generalizations in special graph classes
A Krausz (k; m)-partition of a graph G is a decomposition of G into cliques, such that any vertex belongs to at most k cliques and any two cliques have at most m vertices in common. The m-Krausz dimension kdim(m) (G) of the graph G is the minimum number k such that G has a Krausz (k, m) -partition. In particular, 1-Krausz dimension or simply Krausz dimension kdim (G) is a well-known graph-theoretical parameter. In this paper we prove that the problem "kdim (G)  = 1, but the problem "kdim(m) (G)  = 1
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