Equitable partition of plane graphs with independent crossings into induced forests
Abstract
The cluster of a crossing in a graph drawing in the plane is the set of the four endvertices of its two crossed edges. Two crossings are independent if their clusters do not intersect. In this paper, we prove that every plane graph with independent crossings has an equitable partition into $m$ induced forests for any $m\geq 8$. Moreover, we decrease this lower bound 8 for $m$ to 6, 5, 4 and 3 if we additionally assume that the girth of the considering graph is at least 4, 5, 6 and 26, respectively.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.08337
 Bibcode:
 2019arXiv190308337N
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics
 EPrint:
 15 Pages