Premium
On spanning trees and walks of low maximum degree
Author(s) -
Sanders Daniel P.,
Zhao Yue
Publication year - 2001
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/1097-0118(200102)36:2<67::aid-jgt2>3.0.co;2-c
Subject(s) - mathematics , spanning tree , combinatorics , degree (music) , vertex (graph theory) , minimum spanning tree , graph , random walk , minimum degree spanning tree , connectivity , discrete mathematics , statistics , physics , acoustics
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 $\lceil {{8-2\chi}\over{3}}\rceil$ and a closed, spanning walk meetting each vertex at most $\lceil {{6-2\chi}\over{3}}\rceil$ times. Each of these results is shown to be best possible. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 67–74, 2001