On the edge chromatic vertex stability number of graphs
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 an...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
20.04.2020
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.2004.10551 |