Naslov
Polycycles and their boundary

Autori
Dutour, Mathieu ; Shtogrin, Mikhail ; Deza, Michel

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
Com2mac Mini-workshop on two-face embeddings of graphs and applications / - , 2004

Skup
Com2mac Mini-workshop on two-face embeddings of graphs and applications

Mjesto i datum
Pohang, Republika Koreja, 05.01.2004. - 14.01.2004

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
polycycles; boundary; embedding

Sažetak
We consider here (p, s)-polycycles}; ; (3<=p<=s) i.e. plane graphs, such that all interior faces are p-gons, all interior vertices are s-valent and any vertex of the boundary (i.e. the exterior face) has valency within [2, s]. The boundary sequence of a (p, s)-polycycle P is the sequence b(P) enumerating, up to a cyclic shift or reversal, the consecutive valencies of vertices of the boundary. We show that the values p=3, 4 are the only ones, such that the boundary sequence defines its (p, 3)-filling}; ; (i.e. a (p, 3)- polycycle with given boundary) uniquely. Also we give new results in the enumeration of maps Mn(p, q) (i.e. plane 3-valent maps with only p- and q- gonal faces, such that the q-gons are organized in an n-ring) and two of their generalizations. Both problems are similar (3-valent filling by p-gons of a boundary or of a ring of q-gons) and the same programs were used for both computations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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