TY - JOUR
ID - 24806
TI - Edge-group choosability of outerplanar and near-outerplanar graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Khamseh, Amir
AD - Department of Mathematics, Kharazmi University, 15719-14911, Tehran, Iran
Y1 - 2020
PY - 2020
VL - 9
IS - 4
SP - 211
EP - 216
KW - List coloring
KW - Group choosability
KW - Edge-group choosability
DO - 10.22108/toc.2020.116355.1633
N2 - 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 $chi'_{gl}(G)leq D$.
UR - https://toc.ui.ac.ir/article_24806.html
L1 - https://toc.ui.ac.ir/article_24806_069756990b05736c896cb48109b43257.pdf
ER -