A New Characterization of Graphs Based on Interception Relations

Abstract

While graphs are normally defined in terms of the 2-place relation of adjacency, we take the 3-place relation of interception as the basic primitive of their definition. The paper views graphs as an economical scheme for encoding interception relations, and establishes an axiomatic characterization of relations that lend themselves to representation in terms of graph interception, thus providing a new characterization of graphs. © 1996 John Wiley & Sons, Inc.