Loading [MathJax]/jax/output/HTML-CSS/jax.js

Robert Berke ; Tibor Szabó - Relaxed Two-Coloring of Cubic Graphs

dmtcs:3445 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3445
Relaxed Two-Coloring of Cubic GraphsConference paper

Authors: Robert Berke 1; Tibor Szabó 1

  • 1 Department of Computer Science [ETH Zürich]

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+ colors such that k parts form an independent set and parts span components of order bounded by a constant. A lot of interesting questions remain open.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: Vertex coloring,bounded size components,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

1 Document citing this article

Consultation statistics

This page has been seen 218 times.
This article's PDF has been downloaded 392 times.