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arXiv · 2004.10551

On the edge chromatic vertex stability number of graphs

Saeid Alikhani·Mohammad R. Piri
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Abstract

For an arbitrary invariant $\rho (G)$ of a graph $G$, the $\rho-$vertex stability number $vs_{\rho}(G)$ is the minimum number of vertices of $G$ whose removal results in a graph $H\subseteq G$ with $\rho (H)\neq \rho (G)$ or with $E(H)=\varnothing$. In this paper, first we give some general lower and upper bounds for the $\rho$-vertex stability number, and then study the edge chromatic stability number of graphs, $vs_{\chi^{\prime}}(G)$, where $\chi^{\prime}=\chi^{\prime}(G)$ is edge chromatic number (chromatic index) of $G$. We prove some general results for this parameter and determine $vs_{\chi^{\prime}}(G)$ for specific classes of graphs.

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Saeid Alikhani, Mohammad R. Piri. 2020-04-20. On the edge chromatic vertex stability number of graphs. https://arxiv.org/abs/2004.10551

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