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

As a corollary, we prove that for every positive integer t, if a graph G has no Kt+1 minor, then its vertex set V(G) can be partitioned into 3t sets X1,…,X3t such that for each i, the subgraph induced on Xi has no component of size larger than a function of t. This corollary improves a result of Wood (2010) [21], which states that V(G) can be partitioned into ⌈3.5t+2⌉ such sets.