Online graph coloring with bichromatic exchanges

Sylvain Gravier 1 Marc Heinrich 2
2 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : Greedy algorithms for the graph coloring problem require a large number of colors, even for very simple classes of graphs. For example, any greedy algorithm coloring trees requires Ω(log n) colors in the worst case. We consider a variation of greedy algorithms in which the algorithm is allowed to make modifications to previously colored vertices by performing local bichromatic exchanges. We show that such algorithms can be used to find an optimal coloring in the case of bipartite graphs, chordal graphs and outerplanar graphs. We also show that it can find colorings of general planar graphs with O(log ∆) colors, where ∆ is the maximum degree of the graph. The question of whether planar graphs can be colored by an online algorithm with bichromatic exchanges using only a constant number of colors is still open.
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02167055
Contributor : Marc Heinrich <>
Submitted on : Thursday, June 27, 2019 - 1:42:09 PM
Last modification on : Thursday, November 21, 2019 - 2:17:27 AM

File

Bichromatic_Exchange(2).pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02167055, version 1

Citation

Sylvain Gravier, Marc Heinrich. Online graph coloring with bichromatic exchanges. 2019. ⟨hal-02167055⟩

Share

Metrics

Record views

102

Files downloads

52