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arXiv · 2610.24117

PArcK trees can get as hot as you want

Svenja Huntemann·Neil A. McKay·Craig Tennenhouse
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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.

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Svenja Huntemann, Neil A. McKay, Craig Tennenhouse. 2026-10-16. PArcK trees can get as hot as you want. https://arxiv.org/abs/2610.24117

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