Subh: A game on digraphs

There are many interesting games on graphs [?]. This paper describes a new game which incorporates a new idea. In traditional games on graphs, the two players alternately choose edges such that the rst player wants to attain a property and the second player wants to attain a similar property. For example in Sim [?], the two players alternately color an edge (in a complete graph on six nodes) with either red or blue. (The rst player chooses the color red and the second player chooses the color blue.) The rst player's aim is to get a red triangle and the second player's aim is to get a blue triangle. (By a triangle, we mean a cycle of length three.) The person who gets a triangle of his color wins. The game presented in this paper is di erent from the traditional ones in the sense that one player pursues a property while the other player tries to block it.