The Circular Dimension of a Graph.
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A contribution to the abstract theory of graphs. A graph G is an ordered pair (V, I), where V is a nonempty collection of vertices and I is a reflexive and symmetric binary relation of adjacency on V. There is a collection of functions that maps each vertex of V into an arc on a fixed circle. The circular dimension of G is defined as the smallest integer m such that G has an m-arc intersection model. A graph is complete partite if its vertices can be partitioned into disjoint classes so that any 2 vertices from the same class are nonadjacent, while any 2 vertices from different classes are adjacent. This paper establishes that the maximum circular dimension of any complete partite graph having n vertices is the largest integer p such that 2 (exp p) + p is less than or equal to n + 1. 24 pp. Bibliog. (MW)
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