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Chen, Y. and Dai, G. (2022) Binding Number and Path-Factor Critical Deleted Graphs. AKCE International Journal of Graphs and Combinatorics, 19, 197-200.
https://doi.org/10.1080/09728600.2022.2094299

has been cited by the following article:

• TITLE: Binding Number and Fractional k-Factors of Graphs

  AUTHORS: Renying Chang

  KEYWORDS: Binding Number, Fractional k-Factor, Fractional Matching, Independent Set, Covering Set

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.7, July 29, 2024

  ABSTRACT: In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind( G )=min{ | N G ( X ) | | X | :∅≠X⊆V( G ) } . It is proved that a graph G has a fractional 1-factor if bind( G )≥1 and has a fractional k-factor if bind( G )≥k− 1 k . Furthermore, it is showed that both results are best possible in some sense.