In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either only one vertex or only one hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed. When a player chooses to remove one hyperedge, only that chosen hyperedge is removed. Whoever removes the last vertex wins the game. Following from the winning strategy for Take-Away Impartial Combinatorial Games on Oddly Uniform or Evenly Uniform Hypergraphs, this talk is about the new winning strategy for the Take-Away Games on neither Oddly nor Evenly Uniform Hypergraphs. These neither Oddly nor Evenly Uniform Hypergraphs, however, have to satisfy the specific given requirements.

Zoom Link: https://ncsu.zoom.us/j/98139608681?pwd=Z3RnRGRYL3JCRnlNT0NFdmZLRzRtdz09