Summary: Restricted colorings of graphs
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
and Bellcore, Morristown, NJ 07960, USA
The problem of properly coloring the vertices (or edges) of a graph using for each vertex
(or edge) a color from a prescribed list of permissible colors, received a considerable amount of
attention. Here we describe the techniques applied in the study of this subject, which combine
combinatorial, algebraic and probabilistic methods, and discuss several intriguing conjectures
and open problems. This is mainly a survey of recent and less recent results in the area, but it
contains several new results as well.
Research supported in part by a United States Israel BSF Grant. Appeared in "Surveys in Combinatorics",
British Combinatorial Conference, London Mathematical Society Lecture Notes Series 187, edited by K.
Walker, Cambridge University Press, 1993, 1-33.