Linear-time algorithm for the unbiased claw game on general graphs

Establish whether the unbiased claw game on arbitrary graphs admits a linear-time algorithm.

Background

The paper provides an O(|V(G)|^3)-time algorithm for the unbiased claw game on general graphs and a linear-time algorithm for the portions that can be reduced to claw-connected graphs of maximum degree different from three. The remaining maximum-degree-three components prevent the authors from obtaining a linear-time algorithm for all graphs.

The authors explicitly leave the existence of a linear-time algorithm on general graphs unresolved; resolving the maximum-degree-three case would settle this broader question.