Functions and line digraphs

Abstract

AbstractConsider two maps f and g from a set E into a set F such that f(x) ≠ g(x) for every x in E. Suppose that there exists a positive integer n such that for any element z in F either f−1(z) or g−1(z) has at most n elements. Then, E can be partitioned into 2n + 1 subsets E1, E2,…,E2n + 1 such that f(Ei)∩ g(Ei) = ϕ, 1 ≤ i ≤ 2n + 1. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 296–303, 2003