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New bounds on the classical and quantum communication complexity of some graph properties *

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32nd Int'l Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012
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unpublished

We study the communication complexity of a number of graph properties where the edges of the graph G are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are: An Ω(n) lower bound on the quantum communication complexity of deciding whether an n-vertex graph G is connected, nearly matching the trivial classical upper bound of O(n log n) bits of communication. A deterministic upper bound of O(n 3/2 log n) bits for deciding if a bipartite graph

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