Independent systems of representatives in weighted graphs

@article{Aharoni2007IndependentSO,
title={Independent systems of representatives in weighted graphs},
author={Ron Aharoni and Eli Berger and Ran Ziv},
journal={Combinatorica},
year={2007},
volume={27},
pages={253-267}
}

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… CONTINUE READING