On spanning trees and walks of low maximum degree

This article uses the discharging method to obtain the best possible results that a 3‐connected graph embeddable on a surface of Euler characteristic χ ≤ −46 has a spanning tree of maximum degree at most and a closed, spanning walk meetting each vertex at most times. Each of these results is shown to be best possible. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 67–74, 2001