Independent systems of representatives in weighted graphs

  title={Independent systems of representatives in weighted graphs},
  author={Ron Aharoni and Eli Berger and Ran Ziv},
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

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 16 references

Haxell: A condition for matchability in hypergraphs

P E.
Graphs and Combinatorics • 1995
View 7 Excerpts
Highly Influenced

On the Strong Chromatic Number

Combinatorics, Probability & Computing • 2004
View 2 Excerpts

Domination numbers and homology

J. Comb. Theory, Ser. A • 2003
View 2 Excerpts

Triangulated spheres and colored cliques

R. Aharoni, M. Chudnovsky, A. Kotlov
Disc. Comput. Geometry • 2002
View 2 Excerpts

Ziv: A tree version of König’s theorem, Combinatorica

R. Aharoni, R. E. Berger
View 1 Excerpt

A note on vertex list coloring

P. E. Haxell
Combin. Probab. Comput • 2001

Ryser's Conjecture for Tripartite 3-Graphs

Combinatorica • 2001
View 1 Excerpt

The Clique Complex and Hypergraph Matching

Combinatorica • 2001
View 3 Excerpts

Hall's theorem for hypergraphs

Journal of Graph Theory • 2000
View 3 Excerpts

Similar Papers

Loading similar papers…