On tree-partitions of graphs
A graph G admits a tree-partition of width k if its vertex set can be partitioned into sets of size at most k so that the graph obtained by identifying the vertices in each set of the partition, and then deleting loops and parallel edges, is a forest. In the paper, we characterize the classes of graphs (finite and infinite) of bounded tree-partition-width in terms of excluded topological minors.
Publication Source (Journal or Book title)
Ding, G., & Oporowski, B. (1996). On tree-partitions of graphs. Discrete Mathematics, 149 (1-3), 45-58. https://doi.org/10.1016/0012-365X(94)00337-I