Combinatorica

, Volume 27, Issue 3, pp 253–267

Independent systems of representatives in weighted graphs

Authors

    • Department of Mathematics Technion
  • Eli Berger
    • Department of Mathematics Technion
    • Department of MathematicsPrinceton University
  • Ran Ziv
    • Department of Computer ScienceTel-Hai Academic College
Article

DOI: 10.1007/s00493-007-2086-y

Cite this article as:
Aharoni, R., Berger, E. & Ziv, R. Combinatorica (2007) 27: 253. doi:10.1007/s00493-007-2086-y

Abstract

The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set of a graph with maximal degree Δ is partitioned into sets Vi of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each Vi at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell, on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of ISR’s.

Mathematics Subject Classification (2000)

05C15

Copyright information

© Springer-Verlag 2007