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)(s,t)-pseudo partial kk-trees and interval graphs. Our results improve earlier upper bounds on (a,1)-gcol(Ik) and (a,1)-gcol(Ck), where IkIk and CkCk denote the classes of interval and chordal graphs with maximum clique size k+1k+1 respectively. Moreover, the upper bound of (a,1)-gcol(Ik) is tight when kk is a multiple of aa.