Discrete and Continuous Dynamical Systems - S· 2018Q2
An independent set degree condition for fractional critical deleted graphs
- 171citations
- Q2SCImago
- 2018year
Short summary
This paper establishes a new degree condition for a graph to be a fractional critical deleted graph, specifically when the maximum degree of any independent set of size $i$ meets a certain threshold.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces a new degree condition for fractional critical deleted graphs.
- The condition relates the maximum degree of independent sets to graph properties.
- The derived result is shown to be tight, meaning it cannot be improved.
- Applies to graphs with specific constraints on integer-valued functions $g$ and $f$.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let $i≥2$, $Δ≥0$, $1≤ a≤ b-Δ$, $n>\frac{(a+b)(ib+2m-2)}{a}+n'$ and $δ(G)≥\frac{b^{2}}{a}+n'+2m$, and let $g,f$ be two integer-valued functions defined on $V(G)$ such that $a≤ g(x)≤ f(x)-Δ≤ b-Δ$ for each $x∈ V(G)$. In this article, it is determined that $G$ is a fractional $(g,f,n',m)$-critical deleted graph if $\max\{d_{1},d_{2},···,d_{i}\}≥\frac{b(n+n')}{a+b}$ for any independent subset $\{x_{1},x_{2},..., x_{i}\}\subseteq V(G)$. The result is tight on independent set degree condition.
The authors' abstract, as published at the source. Discrete and Continuous Dynamical Systems - S, 2018 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics