Locally connected spanning trees in strongly chordal graphs and proper circular-arc graphs
A spanning tree \(T\) of a graph \(G=(V,E)\) is locally connected if for all \(v \in V\) the subgraph of \(G\) induced by \(N_T(v)\) is connected. \textit{L. Cai} [Discrete Appl. Math. 131, 63--75 (2003; Zbl 1022.05079)] showed that it is NP-complete to decide whether a graph has a locally connected spanning tree. Restricted to strongly chordal graphs and circular-arc graphs this problem becomes solvable in linear time, if a simple elimination ordering or arc-intersection model is provided with the input.
scientific article; zbMATH DE number 5124987
scientific article