Connected, Bounded Degree, Triangle Avoidance Games

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 Kn, building up a simple graph. The edges must be chosen according to a set of restrictions R. The winner is the last player to choose an edge that does not violate any of the restrictions in R. For fixed n and R, one of the players has a winning strategy. For a pair of games where R includes bounded degree, connectedness, and triangle-avoidance, we determine the winner for all values of n.