@article{Tian2021, 
author = {Chunyu Tian and Lei Sun},
title = {Partitioning planar graphs with girth at least  9 into an edgeless graph and a graph with bounded size components},
year = {2021},
journal = {Mathematical Modelling and Control},
volume = {1},
number = {3},
pages = {136-144},
keywords = {planar graph, girth, face, vertex partition, discharging procedure},
url = {https://www.sciopen.com/article/10.3934/mmc.2021012},
doi = {10.3934/mmc.2021012},
abstract = {In this paper, we study the problem of partitioning the vertex set of a planar graph with girth restriction into parts, also referred to as color classes, such that each part induces a graph with components of bounded order. An ( I,  Ok)-partition of a graph  G is the partition of  V(G) into two non-empty subsets  V1 and  V2, such that  G[V1] is an edgeless graph and  G[V2] is a graph with components of order at most  k. We prove that every planar graph with girth 9 and without intersecting  9-face admits an ( I,  O6)-partition. This improves a result of Choi, Dross and Ochem (2020) which says every planar graph with girth at least  9 admits an ( I,  O9)-partition.}
}