Two variations of Franklin's theorem

Year, pages: 2007, 61 - 70

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.

Madaras, T. 2007. Two variations of Franklin's theorem. In Tatra Mountains Mathematical Publications, vol. 36, no.2, pp. 61-70. 1210-3195.

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