Breaking intractability of spanning caterpillar tree problem: A logical approach

In 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].