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Journal Articles Journal of Graph Theory Year : 2010

On Vertex Partitions and some Minor-Monotone Parameters

Abstract

We study vertex partitions of graphs according to some minor-monotone graph parameters. Ding et al. [J Combin Theory Ser B 79(2) (2000), 221-246] proved that some minor-monotone parameters ρ are such that, any graph G with ρ(G)⩾2 admits a vertex partition into two graphs with parameter ρ at most ρ(G) − 1. Here we prove that some of these parameters ρ are such that, any graph G with ρ(G)⩾3 admits a vertex partition into three graphs with parameter ρ at most ρ(G) − 2.

Dates and versions

lirmm-00808034 , version 1 (04-04-2013)

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Daniel Gonçalves. On Vertex Partitions and some Minor-Monotone Parameters. Journal of Graph Theory, 2010, 66 (1), pp.49-56. ⟨10.1002/jgt.20490⟩. ⟨lirmm-00808034⟩
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