160 research outputs found
On the Constructor-Blocker Game
In the Constructor-Blocker game, two players, Constructor and Blocker,
alternatively claim unclaimed edges of the complete graph . For given
graphs and , Constructor can only claim edges that leave her graph
-free, while Blocker has no restrictions. Constructor's goal is to build as
many copies of as she can, while Blocker attempts to stop this. The game
ends once there are no more edges that Constructor can claim. The score
of the game is the number of copies of in Constructor's graph at
the end of the game, when both players play optimally and Constructor plays
first. In this paper, we extend results of Patk\'os, Stojakovi\'c and Vizer on
to many pairs of and : We determine when
and , also when both and are odd cycles, using
Szemer\'edi's Regularity Lemma. We also obtain bounds of when
and .Comment: 16 page
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