Excluding Any Graph as a Minor Allows a Low Tree-Width 2-Coloring (2001)
by
Matt Devos
,
Guoli Ding
,
Bogdan Oporowski
,
Daniel P. Sanders
,
Bruce Reed
,
Paul Seymour
,
Dirk Vertigan
| Citations: | 22 - 1 self |
BibTeX
@MISC{Devos01excludingany,
author = {Matt Devos and Guoli Ding and Bogdan Oporowski and Daniel P. Sanders and Bruce Reed and Paul Seymour and Dirk Vertigan},
title = {Excluding Any Graph as a Minor Allows a Low Tree-Width 2-Coloring},
year = {2001}
}
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Abstract
This article proves the conjecture of Thomas that, for every graph G, there is an integer k such that every graph with no minor isomorphic to G has a 2-coloring of either its vertices or its edges where each color induces a graph of tree-width at most k. Some generalizations are also proved.
Citations
| 94 | Quickly excluding a planar graph - Robertson, Seymour, et al. - 1994 |
| 42 | Graph minors. XVI. Excluding a non-planar graph - Robertson, Seymour |
| 37 | Excluding a planar graph - unknown authors - 1986 |
| 20 | Graphs with forbidden subgraphs - Chartrand, Geller, et al. - 1971 |
| 7 | Partitioning graphs of bounded tree-width - Ding, Oporowski, et al. - 1998 |
| 2 | Problem Session of the Third Slovene Conference on Graph Theory - Thomas - 1995 |
