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Oriented list colorings of graphs

✍ Scribed by Zs. Tuza; M. Voigt

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 159 KB
Volume: 36
Category: Article
ISSN: 0364-9024
DOI: 10.1002/1097-0118(200104)36:4<217::aid-jgt1007>3.0.co;2-1

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✦ Synopsis

A 2-assignment on a graph G (V,E) is a collection of pairs Lv of allowed colors speci®ed for all vertices v PV. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satis®es the following property: For every 2-assignment there exists a choice cv PLv for all v PV such that (i) if c(v) c(w), then vw a P E, and (ii) for every ordered pair (a,b) of colors, if some edge oriented from color a to color b occurs, then no edge is oriented from color b to color a. In this paper we characterize the following subclasses of graphs of oriented choice number 2: matchings; connected graphs; graphs containing at least one cycle. In particular, the ®rst result (which implies that the matching with 11 edges has oriented choice number 2) proves a conjecture of Sali and Simonyi.

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