We introduce a family of graph parameters, called induced multipartite graph
parameters, and study their computational complexity. First, we consider the
following decision problem: an instance is an induced multipartite graph
parameter p and a given graph G, and for natural numbers kβ₯2 and
β, we must decide whether the maximum value of p over all induced
k-partite subgraphs of G is at most β. We prove that this problem is
W[1]-hard. Next, we consider a variant of this problem, where we must decide
whether the given graph G contains a sufficiently large induced k-partite
subgraph H such that p(H)β€β. We show that for certain parameters this
problem is para-NP-hard, while for others it is fixed-parameter tractable.Comment: 9 pages, 0 figure