  A spanning generalized caterpillar is a spanning tree in which all vertices
of degree more than two are on a path. In this note, we find a relation between
the existence of spanning generalized caterpillar and the independence and
connectivity number in a graph. We also point out to an error in a "theorem" in
the paper "Spanning spiders and light-splitting switches", by L. Gargano et al.
in Discrete Math. (2004), and find out a relation between another mentioned
theorem and the existence of spanning generalized caterpillar.
