Czechoslovak Mathematical Journal, first online, pp. 1-14
Note on improper coloring of 1-planar graphs
Yanan Chu, Lei Sun, Jun Yue
Received December 7, 2017. Published online June 3, 2019.
Abstract: A graph $G=(V,E)$ is called improperly $(d_1, \dots, d_k)$-colorable if the vertex set $V$ can be partitioned into subsets $V_1, \dots, V_k$ such that the graph $G[V_i]$ induced by the vertices of $V_i$ has maximum degree at most $d_i$ for all $1 \leq i \leq k$. In this paper, we mainly study the improper coloring of 1-planar graphs and show that 1-planar graphs with girth at least 7 are (2,0,0,0)-colorable.
Affiliations: Yanan Chu, Lei Sun (corresponding author), Jun Yue, School of Mathematics and Statistics, Shandong Normal University, No. 1, Daxue Road, Jinan, Shandong, P. R. China, e-mail: firstname.lastname@example.org, Lsun89@163.com, email@example.com