On Spanning 2-trees in a Graph

  title={On Spanning 2-trees in a Graph},
  author={Leizhen Cai},
  journal={Discrete Applied Mathematics},
A k-tree is either a complete graph on k vertices or a graph T that contains a vertex whose neighbourhood in T induces a complete graph on k vertices and whose removal results in a k-tree. A subgraph of a graph is a spanning k-tree if it is a k-tree and contains every vertex of the graph. This paper is concerned with spanning 2-trees in a graph. It is shown that spanning 2-trees have close connections with two special types of spanning trees: locally-connected spanning trees (A locally… CONTINUE READING