Bounded size components—partitions and transversals

Penny Haxell, Tibor Szabó, Gábor Tardos
2003 Journal of combinatorial theory. Series B (Print)  
Answering a question of Alon et al., we show that there exists an absolute constant C such that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the subgraph induced by each part has no component of size greater than C: We obtain similar results for partitioning graphs of given maximum degree into k parts ðk42Þ as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree. r
doi:10.1016/s0095-8956(03)00031-5 fatcat:hsnat4j2f5gzhnyipbgcs4ztjy