2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 199202
author:  Daniela Kühn and Deryk Osthus 

title: 
K
factors in graphs
ℓ


keywords:  graph packing, factor, critical chromatic number 
abstract: 
Let
K
denote the graph obtained from
ℓ

K
by deleting one edge. We show that for every
ℓ
γ>0
and every integer
ℓ≥4
there exists an integer
n
such that every graph
0
=n
0
(γ,ℓ)
G
whose order
n≥n
is divisible by
0
ℓ
and whose minimum degree is at least
(ℓ
contains a
2
3ℓ+1 / ℓ(ℓ2)+γ)n
K
factor, i.e. a collection of disjoint copies of
ℓ

K
which covers all vertices of
ℓ

G
. This is best possible up to the error term
γn
and yields an approximate solution to a conjecture of
Kawarabayashi.

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reference: 
Daniela Kühn and Deryk Osthus (2005),
K
factors in 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.
199202
ℓ


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