Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24493220220901Breaking intractability of spanning caterpillar tree problem: A logical approach147151490710.22060/ajmc.2022.21716.1104ENMasoudKhosravaniAlgoreen Software Ltd. Auckland, New ZealandJournal Article20220802In this paper we pursue a logical approach to prove that the optimisation problem of finding a spanning caterpillar tree in a graph has polynomial algorithm for bounded tree width graphs. A caterpillar (tree) is a tree with the property that if one removes all its leaves only a path is left. To this end we use Courcelle’s theorem and we show how one can present the spanning caterpillar tree problem by using monadic-second order logical expression. The value of this approach reflected better by the fact that finding a spanning caterpillar in a graph is an NP-complete problem [9].https://ajmc.aut.ac.ir/article_4907_c0906e6f5060ef12191f8b5b4b7f51f7.pdf