The cycle-complete graph Ramsey number r ( C 8 , K 8 )
Abstract
The cycle-complete graph Ramsey number
r
(
C
m
,
K
n
)
is the smallest integer
N
such that every graph
G
of order
N
contains a cycle
C
m
on
m
vertices or has independent number
α
(
G
)
≥
n
. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that
r
(
C
m
,
K
n
)
=
(
m
−
1
)
(
n
−
1
)
+
1
for all
m
≥
n
≥
3
(except
r
(
C
3
,
K
3
)
=
6
). In this paper we will present a proof for the conjecture in the case
n
=
m
=
8
.
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