Title: A vertex and edge deletion game on graphs,
Abstract: Starting with a graph, two players take turns in either deleting an edge or
deleting a vertex and all incident edges. The player removing the last vertex
wins. We review the known results for this game and extend the computation of
nim-values to new families of graphs. A conjecture of Khandhawit and Ye on the
nim-values of graphs with one odd cycle is proved. We also see that, for wheels
and their subgraphs, this game exhibits a surprising amount of unexplained
regularity.