%0 Journal Article
%T Edge-group choosability of outerplanar and near-outerplanar graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Khamseh, Amir
%D 2020
%\ 12/01/2020
%V 9
%N 4
%P 211-216
%! Edge-group choosability of outerplanar and near-outerplanar graphs
%K List coloring
%K Group choosability
%K Edge-group choosability
%R 10.22108/toc.2020.116355.1633
%X 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 $Dgeq 5$, then $chi'_{gl}(G)leq D$.
%U https://toc.ui.ac.ir/article_24806_069756990b05736c896cb48109b43257.pdf