Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K3, t-minor-free graphs. Note that any planar graph is K3, 3-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K3, t -minor-free graph has a (t - 1)-tree.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics