Two lower bounds for branching programs
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Size in maximal triangle-free graphs and minimal graphs of diameter 2
Selected papers of the 14th British conference on Combinatorial conference
On lower bounds for read-k-times branching programs
Computational Complexity
Open problems of Paul Erd&ohuml;s in graph theory
Journal of Graph Theory
Communication complexity
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Time-space tradeoffs for branching programs
Journal of Computer and System Sciences
A Non-Linear Time Lower Bound for Boolean Branching Programs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Super-linear time-space tradeoff lower bounds for randomized computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Randomness versus Nondeterminism for Read-Once and Read- k Branching Programs
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
On multi-partition communication complexity
Information and Computation
On the P versus NP intersected with co-NP question in communication complexity
Information Processing Letters
On multi-partition communication complexity
Information and Computation
On the P versus NP intersected with co-NP question in communication complexity
Information Processing Letters
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We show that recognizing the K3-freeness andK4-freeness of graphs is hard, respectively, fortwo-player nondeterministic communication protocols usingexponentially many partitions and for nondeterministic syntacticread-r times branching programs.The key ingredient is ageneralization of a colouring lemma, due to Papadimitriou andSipser, which says that for every balanced redblue colouring of theedges of the complete n-vertex graph there is a set ofεn2 triangles, none of which ismonochromatic, such that no triangle can be formed by picking edgesfrom different triangles. We extend this lemma to exponentiallymany colourings and to partial colourings.