Papers › The only Class 0 Flower snark is the smallest
The only Class 0 Flower snark is the smallest
Guilherme Adamatti Bridi, André Luis Alves Martins, Franklin de Lima Marquezino, Celina Miraglia Herrera de Figueiredo
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Graph pebbling is a game played on graphs with pebbles on their vertices. A pebbling move removes two pebbles from one vertex and places one pebble on an adjacent vertex. The pebbling number is the smallest t so that from any initial configuration of t pebbles it is possible, after a sequence of pebbling moves, to place a pebble on any given target vertex. Graphs whose pebbling number is equal to the number of vertices are called Class~$0$ and provide a challenging set of graphs that resist being characterized. In this note, we answer a question recently proposed by the pioneering study on the pebbling number of snark graphs: we prove that the smallest Flower snark J₃ is Class~$0$, establishing that J₃ is in fact the only Class~$0$ Flower snark.
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