Finding and counting cliques and independent sets in r-uniform hypergraphs

Authors:
Raphael Yuster
Affiliations:
Department of Mathematics, University of Haifa, Haifa, Israel
Venue:
Information Processing Letters
Year:
2006

Citing 3
Cited 2

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WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
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SIAM Journal on Discrete Mathematics

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Abstract

We present a matrix multiplication based algorithm for counting the number of (induced) occurrences of a fixed r-uniform hypergraph in a larger hypergraph. In many cases, the running time is better than that of the naïve algorithm. We also present several useful applications of the algorithm, such as determining the dominant color among monochromatic simplices in a red-blue edge-colored hypergraph, approximating the number of independent simplices in a random hypergraph, and counting induced occurrences of a given 3-uniform k-vertex hypergraph in a larger k-clique free hypergraph.