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Note on “Sharp Isolated Toughness Bound for Fractional ( k,m )-Deleted Graphs”

DOI: 10.4236/jamp.2025.132017, PP. 365-380

Keywords: Graph, Isolated Toughness Variant, Fractional -Deleted Graph

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Abstract:

As an appendix of [Gao et al. Sharp isolated toughness bound for fractional ( k,m ) -deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this work is presented.

References

[1]  Ma, Y. and Liu, G. (2003) Isolated Toughness and the Existence of Fractional Factors, Acta Mathematicae Applicatae Sinica, 26, 133-140. (In Chinese)
https://doi.org/10.3321/j.issn:0254-3079.2003.01.014
[2]  Gao, W., Wang, W. and Chen, Y. (2025) Sharp Isolated Toughness Bound for Fractional-Deleted Graphs. Acta Mathematicae Applicatae Sinica, English Series, 41, 252-269.
https://doi.org/10.1007/s10255-024-1067-x
[3]  Zhou, S. (2009) A Minimum Degree Condition of Fractional-Deleted Graphs. Comptes Rendus. Mathématique, 347, 1223-1226.
https://doi.org/10.1016/j.crma.2009.09.022
[4]  Zhou, S. (2010) A Neighborhood Condition for Graphs to Be Fractional-Deleted Graphs. Glasgow Mathematical Journal, 52, 33-40.
https://doi.org/10.1017/s0017089509990139
[5]  Liu, G. and Zhang, L. (2008) Toughness and the Existence of Fractional k-Factors of Graphs. Discrete Mathematics, 308, 1741-1748.
https://doi.org/10.1016/j.disc.2006.09.048

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