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The first player wins the one-colour triangle avoidance game on 16 vertices
We consider the one-colour triangle avoidance game. Using a high performance computing network, we showed that the first player can win the game on 16 vertices.
The Total Acquisition Number Of The Randomly Weighted Path
There exists a significant body of work on determining the acquisition number at(G) of various graphs when the vertices of those graphs are each initially assigned a unit weight. We determine properties of the acquisition number of the path, star, complete, complete bipartite, cycle, and wheel graphs for variations on this initial weighting scheme, with the majority of our work focusing on the expected acquisition number of randomly weighted graphs. In particular, we bound the expected acquisition...
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