An independent set degree condition for fractional critical deleted graphs

By Wei Gao, Juan Luis García Guirao, M. Abdel-Aty, Wenfei Xi. Discrete and Continuous Dynamical Systems. Series A, 2019

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Let \begin{document}$i≥2$ \end{document} , \begin{document}$Δ≥0$ \end{document} , \begin{document}$1≤ a≤ b-Δ$ \end{document} , \begin{document}$n>\frac{(a+b)(ib+2m-2)}{a}+n'$ \end{document} and \begin{document}$δ(G)≥\frac{b^{2}}{a}+n'+2m$ \end{document} , and let \begin{document}$g,f$ \end{document} be two integer-valued functions defined on \begin{document}$V(G)$ \end{document} such that \begin{document}$a≤ g(x)≤ f(x)-Δ≤ b-Δ$ \end{document} for each \begin{document}$x∈ V(G)$ \end{document} . In this article, it is determined that \begin{document}$G$ \end{document} is a fractional \begin{document}$(g,f,n',m)$ \end{document} -critical deleted graph if \begin{document}$\max\{d_{1},d_{2},···,d_{i}\}≥\frac{b(n+n')}{a+b}$ \end{document} for any independent subset \begin{document}$\{x_{1},x_{2},..., x_{i}\}\subseteq V(G)$ \end{document} . The result is tight on independent set degree condition.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bac31dbad1ecf2593fc9ab4b540f8a01abf7d189

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