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

Chun Hung Liu, Sang il Oum

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)133-138
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume49
DOIs
StatePublished - Nov 2015

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Coloring
  • Graph minors
  • Partitioning

Fingerprint Dive into the research topics of 'Partitioning H-minor free graphs into three subgraphs with no large components'. Together they form a unique fingerprint.

  • Cite this