Partitioning H-minor free graphs into three subgraphs with no large components Academic Article

abstract

• 2015 Elsevier B.V. We prove that for every graph H, if a graph G has no H minor, then V(G) can be partitioned into three sets such that the subgraph induced on each set has no component of size larger than a function of H and the maximum degree of G. This answers a question of Esperet and Joret and improves a result of Alon, Ding, Oporowski and Vertigan and a result of Esperet and Joret. As a corollary, for every positive integer t, if a graph G has no Kt+1 minor, then V(G) can be partitioned into 3t sets such that the subgraph induced on each set has no component of size larger than a function of t. This corollary improves a result of Wood.

authors

• Liu, Chun-Hung

published proceedings

• Electronic Notes in Discrete Mathematics

author list (cited authors)

• Liu, C., & Oum, S.

citation count

• 2

complete list of authors

• Liu, Chun-Hung||Oum, Sang-il

publication date

• January 2015

publisher

• Elsevier  Publisher

published in

• Electronic Notes in Discrete Mathematics  Journal

Digital Object Identifier (DOI)

• 10.1016/j.endm.2015.06.020

start page

• 133

end page

• 138

volume

• 49

URL

• http://dx.doi.org/10.1016/j.endm.2015.06.020