In a 2011 paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems was to classify solvable trees. In this paper, we extend this classification to several infinite classes of caterpillars. We also give the maximum number of pegs that can be left on such caterpillars under the restriction that we jump whenever possible.
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