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{\bf Nishali Mehta and \'Akos Seress}
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{\bf Connected, Bounded Degree, Triangle Avoidance Games}
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We consider variants of the triangle-avoidance game first defined by
Harary and rediscovered by Hajnal a few years later. A graph game
begins with two players and an empty graph on $n$ vertices. The two
players take turns choosing edges within $K_{n}$, building up a simple
graph. The edges must be chosen according to a set of restrictions
$\mathcal{R}$. The winner is the last player to choose an edge that
does not violate any of the restrictions in $\mathcal{R}$. For fixed
$n$ and $\mathcal{R}$, one of the players has a winning strategy. For
a pair of games where $\mathcal{R}$ includes bounded degree,
connectedness, and triangle-avoidance, we determine the winner for all
values of $n$.
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