2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 245-250
| author: | Jaroslav Nešetřil and Yared Nigussie |
|---|---|
| title: | Density of universal classes of series-parallel graphs |
| keywords: | circular chromatic number, homomorphism, series-parallel graphs, universality |
| abstract: |
A class of graphs
C
C
C
k
k
-colorable graphs, for any fixed
k≥3
, induces a universal partial order. In [HN1], a
surprisingly small subclass of
C
3
K
-minor-free graphs (
4
G
/K
4
a/b ∈[2,8/3]∪{3}
, there is a
K
-minor-free graph with circular chromatic number
equal to
4
a/b
. In this note we show for each rational number
a/b
within this interval the class
K
a/b
K
-minor-free graphs with circular chromatic number
4
a/b
is universal if and only if
a/b ≠2
,
5/2
or
3
. This shows yet another surprising richness of the
K
-minor-free class that it contains universal classes
as dense as the rational numbers.
4
|
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| reference: | Jaroslav Nešetřil and Yared Nigussie (2005), Density of universal classes of series-parallel 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. 245-250 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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Automatically produced on Di Sep 27 10:09:55 CEST 2005 by gustedt
