Regions without complex zeros for chromatic polynomials on graphs with bounded degree

Combinatorics Probability and Computing

Volumn 17, Issue 2, 2008, Pages 225-238

  Fernández, Roberto ^a   Procacci, Aldo ^a,b  

^a UNIVERSITÉ DE ROUEN   (France)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

POLYNOMIALS;

BOUNDED DEGREE; CHROMATIC POLYNOMIAL;

GRAPH THEORY;

EID: 39449093345     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548307008632     Document Type: Article

References (12)

1. Borgs, C. (2006) Absence of zeros for the chromatic polynomial on bounded degree graphs. Combin. Probab. Comput. 15 63-74.
2. Brydges, D. C. (1984) A short cluster in cluster expansions. In Critical Phenomena, Random Systems, Gauge Theories (K. Osterwalder and R. Stora, eds), Elsevier, pp. 129-83.
3. Cammarota, C. (1982) Decay of correlations for infinite range interactions in unbounded spin systems. Comm. Math. Phys. 85 517-28.
4. Dobrushin, R. L. (1996) Estimates of semi-invariants for the Ising model at low temperatures. In Topics in Statistics and Theoretical Physics. Amer. Math. Soe. Transi. Ser. 2 177 59-81.
5. Gruber, C. and Kunz, H. (1971) General properties of polymer systems. Comm. Math. Phys. 22 133-61.
6. Fernández, R. and Procacci, A. (2007) Cluster expansions for abstract polymer models: New bounds from an old approach. Preprint arXiv math-ph/0605041; Comm. Math. Phys. 274 123-40.
7. Kotecký, R. and Preiss, D. (1986) Cluster expansion for abstract polymer models. Comm. Math. Phys. 103 491-498.
8. Penrose, O. (1967) Convergence of fugacity expansions for classical systems. In Statistical Mechanics: Foundations and Applications (A. Bak, ed.), Benjamin, New York.
9. Procacci, A. and Scoppola, B. (1999) Polymer gas approach, to N-body lattice systems. J. Statist. Phys. 96 49-68.
10. Procacci, A., Scoppola, B. and Gerasimov, V. (2003) Potts model on infinite graphs and the limit of chromatic polynomials. Comm. Math. Phys. 235 215-31.
11. Ruelle, D. (1969) Statistical Mechanics: Rigorous Results, Benjamin, New York/Amsterdam.
12. Sokal, A. (2001) Bounds on the complex zeros of (di)chromatic polynomials and Potts-model partition functions. Combin. Probab. Comput. 10 41-77.