Filling of a given boundary by p-gons and related problems

Discrete Applied Mathematics

Volumn 156, Issue 9, 2008, Pages 1518-1535

  Dutour Sikirić, Mathieu ^a   Deza, Michel ^b   Shtogrin, Mikhail ^c  

^a RUDER BO KOVI INSTITUTE   (Croatia)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Boundary; Enumeration; Plane graphs; Unicity

Indexed keywords

COMPUTATION THEORY; PROBLEM SOLVING;

BOUNDARY SEQUENCE; PLANE GRAPHS;

GRAPH THEORY;

EID: 41549127465     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.11.020     Document Type: Article

References (20)

1. Brinkmann G., Caporossi G., and Hansen P. A constructive enumeration of fusenes and benzenoids. J. Algorithms 45 2 (2002) 155-166
2. Brinkmann G., Delgado Friedrichs O., Dress A., and Harmuth T. CaGe-a virtual environment for studying some special classes of large molecules. MATCH: Comm. Math. Comput. Chem. 36 (1997) 233-237
3. Deza M., and Dutour M. Zigzag structure of simple two-faced polyhedra. Combin. Probab. Comput. 14 1-2 (2005) 31-57
4. 1-embeddable polyhedra. In: Shum K.P., et al. (Ed). Algebras and Combinatorics: An International Congress (1999), ICAC-97 Hong Kong, Springer, Singapore 189-210
5. Deza M., and Grishukhin V.P. Maps of p-gons with a ring of q-gons. Bull. Inst. Combin. Appl. 34 (2002) 99-110
6. Deza M., and Shtogrin M.I. Clusters of cycles. J. Geom. Phys. 40 3-4 (2001) 302-319
7. Deza M., and Shtogrin M.I. Extremal and non-extendible polycycles. Proc. Steklov Inst. Math. 239 (2002) 117-135
8. M. Dutour, PlanGraph. 〈http://www.liga.ens.fr/∼dutour/PlanGraph/〉.
9. Fowler P.W., and Cremona J.E. Fullerenes containing fused triples of pentagonal rings. J. Chem. Soc. Faraday Trans. 93 13 (1997) 2255-2262
10. Fowler P.W., and Manolopoulos D.E. An Atlas of Fullerenes (1995), Clarendon Press, Oxford
11. The GAP Group, GAP-Groups, Algorithms, and Programming, vol. 4, no. 3, 2002.
12. Grünbaum B., and Motzkin T.S. The number of hexagons and the simplicity of geodesics on certain polyhedra. Canad. J. Math. 15 (1963) 744-751
13. R. Hajduk, R. Soták, On the azulenoids with large ring of 7-gons, Manuscript, 2004.
14. T. Harmuth, CPF. 〈http://people.freenet.de/thomas.harmuth/〉.
15. T. Harmuth, personal communication, June 2000.
16. O'Keefe M., and Hyde B.G. Crystal Structures (1996), Mineralogical Society of America, Washington, DC
17. Kirby E.C. On toroidal azulenoids and other shapes of fullerene cages. Fullerene Sci. Technol. 2 (1994) 395-404
18. Klein D.J. Elementary benzenoids. J. Chem. Inform. Comput. Sci. 34 (1994) 453-459
19. T. Madaras, R. Soták, More maps of p-gons with a ring of q-gons, Manuscript, 2004.
20. Malkevich J. A survey of 3-valent 3-polytopes with two types of faces. In: Guy R., et al. (Ed). Proceedings of Calgary International Conference on Combinatorial Structures and their Applications (1970), Gordon and Breach, New York 255-256