The circular dimension of a graph |
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Authors: | Robert B Feinberg |
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Institution: | Mathematics Department, Iowa State University, Ames, IA 50011, U.S.A. |
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Abstract: | A graph is a pair (V, I), V being the vertices and I being the relation of adjacency on V. Given a graph G, then a collection of functions {fi}mn=1, each fi mapping each vertex of V into anarc on a fixed circle, is said to define an m-arc intersection model for G if for all x,y ? V, xly ? (∨i?m)(fi(x)∩fi(y)≠Ø). The circular dimension of a graph G is defined as the smallest integer m such that G has an m-arc intersection model. In this paper we establish that the maximum circular dimension of any complete partite graph having n vertices is the largest integer p such that 2p+p?n+1. |
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