Activation strategy for asymmetric marking games

This paper extends the widely used activation strategy of the marking game on graphs to asymmetric marking games. The extended activation strategy is then applied to asymmetric marking games on chordal graphs, (s, t)-pseudo partial k-trees and interval graphs. Our results improve earlier upper bounds on (a, 1)gcol (Ik) and (a, 1)-gcol (Ck), where Ik and Ck denote the classes of interval and chordal graphs with maximum clique size k + 1 respectively. Moreover, the upper bound of (a, 1)-gcol (Ik) is tight when k is a multiple of a. ∗This research was partially supported by the Educational Department of Fujian Province of China under grant JA05181, and SRF for ROCS of SEM. †This research was partially supported by the National Science Council under grant NSC95-2115M-110-013-MY3