Connected Subtraction Games on Subdivided Stars

TL;DR

This paper studies connected subtraction games on graphs, extending takeaway games, and establishes periodicity results especially for subdivided star graphs.

Contribution

It introduces general periodicity results for connected subtraction games and provides specific findings for subdivided star graphs.

Findings

Derived general periodicity results for connected subtraction games.

Established specific results for subdivided star graphs.

Extended the theory of takeaway games to connected graphs.

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.