Geodesic
The graph grabbing game on blow-ups of trees and cycles
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 895-907

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The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed vertices at the end of the game when all vertices have been claimed. Seacrest and Seacrest conjectured that Alice can secure at least half of the total weight of every weighted connected bipartite even graph. Later, Egawa, Enomoto and Matsumoto partially confirmed this conjecture by showing that Alice wins the game on a class of weighted connected bipartite even graphs called K_m,n-trees. We extend the result on this class to include a number of graphs, e.g. even blow-ups of trees and cycles.
Keywords: games on graphs, two-player games, graph grabbing games, blow-ups of graphs 
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Boriboon, Sopon; Kittipassorn, Teeradej. The graph grabbing game on blow-ups of trees and cycles. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 4, pp. 895-907. http://geodesic.mathdoc.fr/item/DMGT_2023_43_4_a1/