Naslov
Zigzag structures of simple two-faced polyhedra

Autori
Deza, Mathieu ; Dutour, Mathieu

Izvornik
Combinatorics probability & computing (0963-5483) 14 (2005), 1/2; 31-57

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
plane graphs; groups; zigzags; railroads; extremal problems

Sažetak
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigzag and railroad structures of general 3-valent plane graph and, especially, of simple two-faced polyhedra, i.e., 3-valent 3-polytopes with only a-gonal and b-gonal faces, where 3 <= a < b <= 6 ; the main cases are (a, b)=(3, 6), (4, 6) and (5, 6) (the fullerenes). We completely describe the zigzag structure for the case (a, b)=(3, 6). For the case (a, b)=(4, 6) we describe symmetry groups, classify all tight graphs with simple zigzags and give the upper bound 9 for the number of zigzags in general tight graphs. For the remaining case (a, b)=(5, 6) we give a construction realizing a prescribed zigzag structure.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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