2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 245250
author:  Jaroslav Nešetřil and Yared Nigussie 

title:  Density of universal classes of seriesparallel graphs 
keywords:  circular chromatic number, homomorphism, seriesparallel 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
minorfree graphs (
4
G
/K
4
a/b ∈[2,8/3]∪{3}
, there is a
K
minorfree 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
minorfree 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
minorfree 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 seriesparallel 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. 245250 
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