Partitioning into graphs with only small components
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