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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{huntemann2026parck,
  title = {{PArcK trees can get as hot as you want}},
  author = {Svenja Huntemann and Neil A. McKay and Craig Tennenhouse},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24117},
  eprint = {2610.24117},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24117},
}
RIS
TY  - UNPB
TI  - PArcK trees can get as hot as you want
AU  - Svenja Huntemann
AU  - Neil A. McKay
AU  - Craig Tennenhouse
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.24117
UR  - https://arxiv.org/abs/2610.24117
AB  - 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.
ER  -