On the communication complexity of graph properties
András Sándor Hajnal, Wolfgang Maaß, György Turán · 1988
We prove θ(n log n) bounds for the deterministic 2-way communication complexity of the graph properties CONNECTIVITY, s-t-CONNECTIVITY and BIPARTITENESS (for arbitrary partitions of the variables into two sets of equal size). The proofs are based on combinatorial results of Dowling-Wilson and Lovász-Saks about partition matrices using the Möbius function, and the Regularity Lemma of Szemerédi. The bounds imply improved lower bounds for the VLSI complexity of these decision problems and sharp bounds for a generalized decision tree model which is related to the notion of evasiveness.