On-Line Choice Number of Complete Multipartite Graphs: an Algorithmic Approach

This paper studies the on-line choice number of complete multipartite graphs with independence number m. We give a unified strategy for every prescribed m. Our main result leads to several interesting consequences comparable to known results. (1) If k1− m ∑ p=2 ( p2 2 − 3p 2 + 1 ) kp > 0, where kp denotes the number of parts of cardinality p, then G is on-line chromatic-choosable. (2) If |V (G)| 6 m2−m+2 m2−3m+4χ(G), then G is on-line chromatic-choosable. (3) The on-line choice number of regular complete multipartite graphs Km?k is at most ( m+ 12 − √ 2m− 2 ) k for m > 3.