Enzo Marinari and Guilhem Semerjian J. Stat. Mech. (2006) P06019 doi:10.1088/1742-5468/2006/06/P06019
Enzo Marinari1 and Guilhem Semerjian2
Show affiliationsWe apply in this paper (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.
E-print Number: cond-mat/0603657
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05.20.Gg Classical ensemble theory
Issue 06 (June 2006)
Received 27 March 2006, accepted for publication 6 June 2006
Published 29 June 2006
Enzo Marinari and Guilhem Semerjian J. Stat. Mech. (2006) P06019
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Brian L Tierney et al 2007 J. Phys.: Conf. Ser. 78 012075
A. Glatz et al 2008 EPL 82 47002
A. Glatz and I. S. Beloborodov 2009 EPL 87 57009
Dan Milisavljevic et al. 2008 ApJ 684 1170
Guilhem Semerjian and Martin Weigt 2004 J. Phys. A: Math. Gen. 37 5525
S. Blondin et al. 2008 ApJ 682 724
G. Miknaitis et al. 2007 ApJ 666 674
Claes Fransson et al. 2005 ApJ 622 991