Connected Subtraction Games on Subdivided Stars
Combinatorics
2026-04-17 v1 Discrete Mathematics
Abstract
The present paper deals with connected subtraction games in graphs, which are generalization of takeaway games. In a connected subtraction game, two players alternate removing a connected sub-graph from a given connected game-graph, provided the resulting graph is connected, and provided the number of vertices of the removed subgraph belongs to a prescribed set of integers. We derive general periodicity results on such games, as well as specific results when played on subdivided stars.
Keywords
Cite
@article{arxiv.1807.10468,
title = {Connected Subtraction Games on Subdivided Stars},
author = {Antoine Dailly and Julien Moncel and Aline Parreau},
journal= {arXiv preprint arXiv:1807.10468},
year = {2026}
}