Spanning trees in 3-connected K3,t-minor-free graphs

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 Barnetteʹs result for the direction of K 3 , t -minor-free graphs. Note that any planar graph is K 3 , 3 -minor-free. Actually, we show that for an even integer t ⩾ 3 , any 3-connected K 3 , t -minor-free graph has a ( t − 1 ) -tree.