Injective edge coloring of graphs
| Autor: | Pedro J. Cruz, Domingos M. Cardoso, Orestes J. Cerdeira, Charles Dominicc |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | Three edges $e_{1}, e_{2}$ and $e_{3}$ in a graph $G$ are consecutive if they form a path (in this order) or a cycle of lengths three. An injective edge coloring of a graph $G = (V,E)$ is a coloring $c$ of the edges of $G$ such that if $e_{1}, e_{2}$ and $e_{3}$ are consecutive edges in $G$, then $c(e_{1})\neq c(e_3)$. The injective edge coloring number $\chi_{i}^{'}(G)$ is the minimum number of colors permitted in such a coloring. In this paper, exact values of $\chi_{i}^{'}(G)$ for several classes of graphs are obtained, upper and lower bounds for $\chi_{i}^{'}(G)$ are introduced and it is proven that checking whether $\chi_{i}^{'}(G)= k$ is NP-complete. in publication |
| Databáze: | OpenAIRE |
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