✦ LIBER ✦

Functions and line digraphs

✍ Scribed by Amine El Sahili

Book ID: 102342540
Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 84 KB
Volume: 44
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10146

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Consider 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 2__n__ + 1 subsets E~1~, E~2~,…,E~2__n__ + 1~ such that f(E~i~)∩ g(E~i~) = ϕ, 1 ≤ i ≤ 2__n__ + 1. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 296–303, 2003

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