TY  JOUR
AU1  Pei, Chaoping
AU2  Chen, Ming
AU3  Li, Yusheng
AU4  Yu, Pei
AB  A connected graph H with
$$H\ge \sigma (G)$$

H

≥
σ
(
G
)
is said to be Ggood if
$$R(G,H)=(\chi (G)1)(H1)+\sigma (G)$$
R
(
G
,
H
)
=
(
χ
(
G
)

1
)
(

H


1
)
+
σ
(
G
)
. For an integer
$$\ell \ge 3$$
ℓ
≥
3
, let
$$P_\ell $$
P
ℓ
be a path of order
$$\ell $$
ℓ
, and
$$H^{(\ell )}$$
H
(
ℓ
)
a graph obtained from H by joining the end vertices of
$$P_\ell $$
P
ℓ
to distinct vertices u, v of H. It is widely known that for any graphs G and H, if
$$\ell $$
ℓ
is sufficiently large, then
$$H^{(\ell )}$$
H
(
ℓ
)
is Ggood. In this note, we show that there exists a constant
$$c=c(\Delta )$$
c
=
c
(
Δ
)
such that for any graphs G and H with
$$\Delta (G)\le \Delta $$
Δ
(
G
)
≤
Δ
and
$$\Delta (H)\le \Delta $$
Δ
(
H
)
≤
Δ
, if
$$\ell \ge c\cdot (G+H)$$
ℓ
≥
c
·
(

G

+

H

)
, then
$$H^{(\ell )}$$
H
(
ℓ
)
is Ggood; and if
$$n\ge 2\alpha (G)+\Delta ^2(G)+4$$
n
≥
2
α
(
G
)
+
Δ
2
(
G
)
+
4
, then
$$P_n$$
P
n
is Ggood.
TI  Ramsey Good Graphs with Long Suspended Paths
JF  Graphs and Combinatorics
DO  10.1007/s003730181910z
DA  20180606
UR  https://www.deepdyve.com/lp/springerjournals/ramseygoodgraphswithlongsuspendedpathsle9tnnNqhy
SP  759
EP  767
VL  34
IS  4
DP  DeepDyve