Author:
Vito V,Nabila A C,Safitri E,Silaban D R
Abstract
Abstract
Given simple graphs F, G, and H, we write F → (G, H) if for every red-blue coloring of the edges of F, there exists either a red subgraph G or a blue subgraph H in F. The size Ramsey number for G and H, denoted by
r
^
(G, H), is the smallest size of a graph F which satisfies F → (G, H). If in addition F must be connected, then the resulting number is called the connected size Ramsey number for G and H, denoted by
r
^
c
(G, H). In this paper, we obtain upper bounds for
r
^
(
t
K
2
,
P
m
)
,
r
^
c
(
t
K
2
,
P
m
)
,
r
^
(
t
K
2
,
P
4
+
a leaf
)
, and
r
^
c
(
t
K
2
,
P
4
+
a leaf
)
for t ≥ 1 and m ≥ 3. We also determine the exact values of
r
^
c
(
2
K
2
,
P
m
)
and
r
^
(
t
K
2
,
P
3
)
. In addition, the exact values of
r
^
c
(
t
K
2
,
P
3
)
for t = 3,4 are given.
Subject
General Physics and Astronomy
Cited by
2 articles.
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