  A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition 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 {\it $m$-krausz} dimension
$kdim_m(G)$ of the graph $G$ is the minimum number $k$ such that $G$ has a
krausz $(k,m)$-partition. 1-krausz dimension is known and studied krausz
dimension of graph $kdim(G)$.
  In this paper we prove, that the problem $"kdim(G)\leq 3"$ is polynomially
solvable for chordal graphs, thus partially solving the problem of P. Hlineny
and J. Kratochvil. We show, that the problem of finding $m$-krausz dimension is
NP-hard for every $m\geq 1$, even if restricted to (1,2)-colorable graphs, but
the problem $"kdim_m(G)\leq k"$ is polynomially solvable for $(\infty,1)$-polar
graphs for every fixed $k,m\geq 1$.
