  We consider two conjectures made in regard to the graph grabbing game, played
on a vertex weighted graph. Seacrest and Seacrest conjectured in 2012 that the
first player can win the graph grabbing game on any even-order bipartite graph.
Eoh and Choi conjectured a strengthening of this in 2019, namely that the first
player can win on any graph with no induced corona product of an odd cycle and
a point. We provide a family of counterexamples to the latter conjecture, and
propose a weaker conjecture in its place. We also show that the above two
conjectures are equivalent when the vertex weights are all $0$ or $1$.
