An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs

An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs

Improving a result of Sárközy and Selkow, we show that for all integers r,k≥2 there exists a constant n0=n0(r,k) such that if n≥n0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100rlogr+2rk vertex disjoint connected monochr...

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Veröffentlicht in:Journal of graph theory 2013-06, Vol.73 (2), p.127-145
Hauptverfasser: Sárközy, Gábor N., Selkow, Stanley M., Song, Fei
Format: Artikel
Sprache:eng
Schlagworte:
Graph theory
regulatory lemma
Studies
vertex partitions
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Zusammenfassung:Improving a result of Sárközy and Selkow, we show that for all integers r,k≥2 there exists a constant n0=n0(r,k) such that if n≥n0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100rlogr+2rk vertex disjoint connected monochromatic k‐regular subgraphs and vertices. This is close to best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 127–145, 2013
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21661