PArcK trees can get as hot as you want

Source abstract

We consider the combinatorial game Partizan Arc Kayles as a generalization of Domineering. An extensive technical search using genetic algorithms found hot positions of temperature exceeding 2. We discuss this search and construct a family of positions with high temperature that includes these graphs and prove that Partizan Arc Kayles has unbounded temperature. We identify an infinite family of second-player win positions as part of our main construction.