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Two variations of Franklin's theorem

In: Tatra Mountains Mathematical Publications, vol. 36, no. 2
Tomáš Madaras
Detaily:
Rok, strany: 2007, 61 - 70
Kľúčové slová:
plane graph, light graph, face size, induced path
O článku:
P. Franklin proved that each 3-connected plane cubic graph of minimum face size 5 contains a pentagon adjacent to two faces of size at most 6. In this paper we strengthen this theorem proving that there exists a pentagon adjacent to two faces of size at most 6 such that every vertex of these three faces is of degree at most 23; we prove also that there exists a triple of faces with size sum at most 17 such that they form an induced path in the dual graph.
Ako citovať:
ISO 690:
Madaras, T. 2007. Two variations of Franklin's theorem. In Tatra Mountains Mathematical Publications, vol. 36, no.2, pp. 61-70. 1210-3195.

APA:
Madaras, T. (2007). Two variations of Franklin's theorem. Tatra Mountains Mathematical Publications, 36(2), 61-70. 1210-3195.