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 [8-2χ/3] and a closed, spanning walk meetting each vertex at most [6-2χ/3] times. Each of these results is shown to be best possible. © 2001 John Wiley & Sons, Inc

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 chi less than or equal to -46 has a spanning tree of maximum degree at most [8-2 chi / 3] and a closed, spanning walk meetting each vertex at most [6-2 chi / 3] times. Each of these results is shown to be best possible. (C) 2001 John Wiley & Sons, Inc