On the number of circuits in random graphs

Details On the number of circuits in random graphs On the number of circuits in random graphs

2006-03-24

arxiv.org/abs/cond-mat/0603657v1

J. Stat. Mech. P06019 (2006).

Physics

Condensed Matter

Statistical Mechanics

30 pages

Scientific paper

10.1088/1742-5468/2006/06/P06019

We apply in this article (non rigorous) statistical mechanics methods to the problem of counting long circuits in graphs. The outcomes of this approach have two complementary flavours. On the algorithmic side, we propose an approximate counting procedure, valid in principle for a large class of graphs. On a more theoretical side, we study the typical number of long circuits in random graph ensembles, reproducing rigorously known results and stating new conjectures.

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