Partitioning a triangle-free planar graph into a forest and a forest of bounded degree

An (F,Fd)-partition of a graph is a vertex-partition into two sets F and Fd such that the graph induced by F is a forest and the one induced by Fd is a forest with maximum degree at most d. We prove that every triangle-free planar graph admits an (F,F5)-partition. Moreover we show that if for some i...

Full description

Saved in:
Bibliographic Details
Published inEuropean journal of combinatorics Vol. 66; pp. 81 - 94
Main Authors Dross, François, Montassier, Mickael, Pinlou, Alexandre
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2017
Elsevier
Subjects
Computer Science
Discrete Mathematics
Online AccessGet full text

Cover

More Information
Summary:An (F,Fd)-partition of a graph is a vertex-partition into two sets F and Fd such that the graph induced by F is a forest and the one induced by Fd is a forest with maximum degree at most d. We prove that every triangle-free planar graph admits an (F,F5)-partition. Moreover we show that if for some integer d there exists a triangle-free planar graph that does not admit an (F,Fd)-partition, then it is an NP-complete problem to decide whether a triangle-free planar graph admits such a partition.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2017.06.014