@article {
author = {Khamseh, Amir},
title = {Edge-group choosability of outerplanar and near-outerplanar graphs},
journal = {Transactions on Combinatorics},
volume = {9},
number = {4},
pages = {211-216},
year = {2020},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2020.116355.1633},
abstract = {Let $\chi_{gl}(G)$ be the {\it{group choice number}} of $G$. A graph $G$ is called {\it{edge-$k$-group choosable}} if its line graph is $k$-group choosable. The {\it{group-choice index}} of $G$, $\chi'_{gl}(G)$, is the smallest $k$ such that $G$ is edge-$k$-group choosable, that is, $\chi'_{gl}(G)$ is the group chice number of the line graph of $G$, $\chi_{gl}(\ell(G))$. It is proved that, if $G$ is an outerplanar graph with maximum degree $\D<5$, or if $G$ is a $({K_2}^c+(K_1 \cup K_2))$-minor-free graph, then $\chi'_{gl}(G)\leq \D(G)+1$. As a straightforward consequence, every $K_{2,3}$-minor-free graph $G$ or every $K_4$-minor-free graph $G$ is edge-$(\D(G)+1)$-group choosable. Moreover, it is proved that if $G$ is an outerplanar graph with maximum degree $\D\geq 5$, then $\chi'_{gl}(G)\leq \D$.},
keywords = {List coloring,Group choosability,Edge-group choosability},
url = {https://toc.ui.ac.ir/article_24806.html},
eprint = {https://toc.ui.ac.ir/article_24806_069756990b05736c896cb48109b43257.pdf}
}