Abstract
We show that the square of every connected S(K1,4)-free graph satisfying a matching condition has a 2-connected spanning subgraph of maximum degree at most 3. Furthermore, we characterise trees whose square has a 2-connected spanning subgraph of maximum degree at most k. This generalises the results on S(K1,3)-free graphs of Henry and Vogler [7] and Harary and Schwenk [6], respectively.
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