Majority choosability of 1-planar digraph

@article{Xia2023,
abstract = {A majority coloring of a digraph $D$ with $k$ colors is an assignment $\pi \colon V(D) \rightarrow \lbrace 1,2,\cdots ,k\rbrace $ such that for every $v\in V(D)$ we have $\pi (w)=\pi (v)$ for at most half of all out-neighbors $w\in N^+(v)$. A digraph $D$ is majority $k$-choosable if for any assignment of lists of colors of size $k$ to the vertices, there is a majority coloring of $D$ from these lists. We prove that if $U(D)$ is a 1-planar graph without a 4-cycle, then $D$ is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.},
author = {Xia, Weihao, Wang, Jihui, Cai, Jiansheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {majority choosable; OD-3-choosable; 1-planar digraph},
language = {eng},
number = {3},
pages = {663-673},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Majority choosability of 1-planar digraph},
url = {http://eudml.org/doc/299122},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Xia, Weihao
AU - Wang, Jihui
AU - Cai, Jiansheng
TI - Majority choosability of 1-planar digraph
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 663
EP - 673
AB - A majority coloring of a digraph $D$ with $k$ colors is an assignment $\pi \colon V(D) \rightarrow \lbrace 1,2,\cdots ,k\rbrace $ such that for every $v\in V(D)$ we have $\pi (w)=\pi (v)$ for at most half of all out-neighbors $w\in N^+(v)$. A digraph $D$ is majority $k$-choosable if for any assignment of lists of colors of size $k$ to the vertices, there is a majority coloring of $D$ from these lists. We prove that if $U(D)$ is a 1-planar graph without a 4-cycle, then $D$ is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.
LA - eng
KW - majority choosable; OD-3-choosable; 1-planar digraph
UR - http://eudml.org/doc/299122
ER -