On the edge chromatic vertex stability number of graphs
| Autor: | Alikhani, Saeid, Piri, Mohammad R. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages, 1 figure |
| Databáze: | arXiv |
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