Locally connected spanning trees in strongly chordal graphs and proper circular-arc graphs

A locally connected spanning tree of a graph G is a spanning tree T of G   such that the set of all neighbors of vv in T induces a connected subgraph of G   for every v∈V(G)v∈V(G). The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively.