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On Graph Complexity

Published online by Cambridge University Press:  16 August 2006

S. JUKNA
S. JUKNA
Affiliation:
Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania
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Abstract

By the complexity of a graph we mean the minimum number of union and intersection operations needed to obtain the whole set of its edges starting from stars. This measure of graphs is related to the circuit complexity of boolean functions.

We prove some lower bounds on the complexity of explicitly given graphs. This yields some new lower bounds for boolean functions, as well as new proofs of some known lower bounds in the graph-theoretic framework. We also formulate several combinatorial problems whose solution would have intriguing consequences in computational complexity.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 6 , November 2006 , pp. 855 - 876
Copyright
2006 Cambridge University Press

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