Toughness, minimum degree, and spanning cubic subgraphs

Abstract

Abstract Degree conditions on the vertices of a t ‐tough graph G (1 ≤ t < 3) are presented which ensure the existence of a spanning cubic subgraph in G . These conditions are best possible to within a small additive constant for every fixed rational t ∈[1,4/3)∪[2,8/3). © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 119–141, 2004