We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game is started by the breaker. This implies the same in the (2 : 1) biased game also in the maker-start game. It remains open to characterize the maker-win graphs...

We consider a Maker-Breaker type game on the square grid, in which each player takes t points on their tth turn. Maker wins if he obtains n points on a line (in any direction) without any of Breaker’s points between them. We show that, despite Maker’s apparent advantage, Breaker can prevent Maker from winning until about his nth turn. We actually prove a stronger result: Breaker only needs to c...

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns in claiming previously unclaimed edges of a given graph H . Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from achieving his goal. We define a function f on the integers and show that for every d-regular graph G on n vertices there is a graph H with at most f(d)n edges such ...

Title of dissertation: Physics of Breaking Bow Waves: A Parametric Investigation using a 2D+T Wave Maker Eric Maxeiner, Doctor of Philosophy, 2009 Dissertation directed by: Professor James H. Duncan Department of Mechanical Engineering A mechanical 2-dimensional wave maker with a flexible surface was used to create waves similar to those formed at the bow of a moving ship. Utilizing the 2D+T ap...