A sufficient condition for the existence of a k-factor excluding a given r-factor

• Autores: Sizhong Zhou, Lan Xu, Yang Xu
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 1, 2017, págs. 13-20
• Idioma: inglés
• DOI: 10.21042/amns.2017.1.00002
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let G be a graph, and let k,r be nonnegative integers with k≥2. A k-factor of G is a spanning subgraph F of G such that dF(x)=k for each x∈V(G), where dF(x) denotes the degree of x in F. For S⊆V(G), NG(S)=⋃x∈SNG(x). The binding number of G is defined by bind(G)=min{|NG(S)||S|:∅≠S⊂V(G),NG(S)≠V(G)}. In this paper, we obtain a binding number and neighborhood condition for a graph to have a k-factor excluding a given r-factor. This result is an extension of the previous results.