Activation strategy for asymmetric marking games

Abstract

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 ( I k ) and ( a , 1 ) - gcol ( C k ) , where I k and C k denote the classes of interval and chordal graphs with maximum clique size k + 1 respectively. Moreover, the upper bound of ( a , 1 ) - gcol ( I k ) is tight when k is a multiple of a .