On the existence of [formula omitted]-factor—From high-dimensional space perspective

Abstract

In recent years, the relationship between network graph parameters and the existence of specific H-factor has attracted the attention of researchers. The latest research has found that for factor deleted graphs and factor critical graphs, the tight bounds of graph parameters are changing as the low bound of connectivity changes. This work studies the existence of {K1,1,K1,2,Ct}-factor from high-dimensional space perspective. Several surfaces reveal that the dynamic changing of tight parameter (toughness, isolated toughness, sun toughness, binding number) bounds are defined. The precise expression of these surfaces are presented.