Bounded size components: partitions and transversals

Authors:
Penny Haxell;Tibor Szabó;Gábor Tardos
Affiliations:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;Department of Computer Science, ETH Zürich, 8092 Zürich, Switzerland;Alfréd Rényi Institute of Mathematics, Pf 127, H-1364 Budapest, Hungary
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

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Abstract

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 (k 2) as well. A related theorem is also proved about transversals inducing only small components in graphs of a given maximum degree.