@article{Matsumoto_Nagao_2023, title={Feedback Game on Eulerian Graphs: Discrete and Computational Geometry, Graphs, and Games}, volume={21}, url={https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1542}, abstractNote={<p>In this paper,&nbsp;we introduce a two-player impartial game on graphs, called feedback game,&nbsp;which is a variant of generalized geography.&nbsp;Feedback game can be regarded as undirected edge geography with an additional rule&nbsp;that the first player who goes back to the starting vertex wins the game.&nbsp;We consider feedback game on an Eulerian graph&nbsp;since the game ends only by going back to the starting vertex.&nbsp;We first show that it is PSPACE-complete in general to determine the winner of the feedback game on Eulerian graphs even if its maximum degree is at most~4.&nbsp;In the latter half of the paper,&nbsp;we discuss the feedback game on two subclasses of Eulerian graphs, i.e.,&nbsp;triangular grid graphs and toroidal grid graphs.</p>}, number={4}, journal={Thai Journal of Mathematics}, author={Matsumoto, Naoki and Nagao, Atsuki}, year={2023}, month={Dec.}, pages={751–768} }