<i>B</i>-sets and planar maps

Abstract

In this paper we examine the relation between i?-sets, which are a purely set-theoretic concept, and various concepts associated with planar maps, for instance, four-colorings, five-colorings, amiltonian circuits, and Petersen's theorem. Moreover, the introduction of the notion of a i?-set into graph theory enables us to ask questions which may be more tractable than the four-color conjecture and shed light on it.