| author: | Robert Berke and Tibor Szabó |
|---|---|
| title: | Relaxed Two-Coloring of Cubic Graphs |
| keywords: | Vertex coloring, bounded size components |
| abstract: |
We show that any graph of maximum degree at most
3
has a two-coloring, such that one color-class is an
independent set while the other color induces monochromatic
components of order at most
189
. On the other hand for any constant
C
we exhibit a
4
-regular graph, such that the deletion of any
independent set leaves at least one component of order
greater than
C
. Similar results are obtained for coloring graphs of
given maximum degree with
k+ℓ
colors such that
k
parts form an independent set and
ℓ
parts span components of order bounded by a constant.
A lot of interesting questions remain open.
|
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| reference: | Robert Berke and Tibor Szabó (2005), Relaxed Two-Coloring of Cubic Graphs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 341-344 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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| ps-source: | dmAE0166.ps (126 K) |
| pdf-source: | dmAE0166.pdf (121 K) |
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