Vol. 37, No. 1, 1971

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ISSN: 0030-8730
B-sets and planar maps

Sherman K. Stein

Vol. 37 (1971), No. 1, 217–224
Abstract

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

Mathematical Subject Classification 2000
Primary: 05C99
Milestones
Received: 2 March 1970
Revised: 28 August 1970
Published: 1 April 1971
Authors
Sherman K. Stein