The paper presents several results on edge partitions and vertex partitions of graphs into graphs with bounded size components. We show that every graph of bounded tree-width and bounded maximum degree admits such partitions. We also show that an arbitrary graph of maximum degree four has a vertex partition into two graphs, each of which has components on at most 57 vertices. Some generalizations of the last result are also discussed. © 2002 Elsevier Science (USA). All rights reserved.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Alon, N., Ding, G., Oporowski, B., & Vertigan, D. (2003). Partitioning into graphs with only small components. Journal of Combinatorial Theory. Series B, 87 (2), 231-243. https://doi.org/10.1016/S0095-8956(02)00006-0