Surahmat Supangken - Academia.edu (original) (raw)

Uploads

Papers by Surahmat Supangken

Research paper thumbnail of On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices

Graphs and Combinatorics, 2002

For given two graphs G dan H , the Ramsey number RðG; H Þ is the smallest positive integer n such... more For given two graphs G dan H , the Ramsey number RðG; H Þ is the smallest positive integer n such that every graph F of order n must contain G or the complement of F must contain H. In [12], the Ramsey numbers for the combination between a star S n and a wheel W m for m ¼ 4; 5 were shown, namely, RðS n ; W 4 Þ ¼ 2n À 1 for odd n and n ! 3, otherwise RðS n ; W 4 Þ ¼ 2n þ 1, and RðS n ; W 5 Þ ¼ 3n À 2 for n ! 3. In this paper, we shall study the Ramsey number RðG; W m Þ for G any tree T n. We show that if T n is not a star then the Ramsey number RðT n ; W 4 Þ ¼ 2n À 1 for n ! 4 and RðT n ; W 5 Þ ¼ 3n À 2 for n ! 3. We also list some open problems.

Research paper thumbnail of The Ramsey numbers of large cycles versus wheels

Discrete Mathematics, 2006

In this paper we show that the Ramsey number R(C n , W m) = 2n − 1 for even m and n 5m/2 − 1.

Research paper thumbnail of The Ramsey Numbers of Large cycles Versus Odd Wheels

Graphs and Combinatorics, 2008

Research paper thumbnail of The Ramsey number of paths with respect to wheels

Discrete Mathematics, 2005

For graphs G and H , the Ramsey number R(G, H) is the smallest positive integer n such that every... more For graphs G and H , the Ramsey number R(G, H) is the smallest positive integer n such that every graph F of order n contains G or the complement of F contains H. For the path P n and the wheel W m , it is proved that R(P n , W m) = 2n − 1 if m is even, m 4, and n (m/2)(m − 2), and R(P n , W m) = 3n − 2 if m is odd, m 5, and n (m − 1/2)(m − 3).

Research paper thumbnail of The Ramsey numbers of fans versus K 4

Research paper thumbnail of Total vertex irregular labeling of complete bipartite graphs

Research paper thumbnail of An Upper Bound for the Ramsey Number of a Cycle of Length Four Versus Wheels

Lecture Notes in Computer Science, 2005

For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that ... more For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that every graph F of n vertices satisfies the following property: either F contains G or the complement of F contains H. In this paper, we show that the Ramsey number R (C 4, ...

Research paper thumbnail of An upper bound for the ramsey number of a cycle of length four versus wheels

For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that ... more For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that every graph F of n vertices satisfies the following property: either F contains G or the complement of F contains H. In this paper, we show that the Ramsey number R (C 4, ...

Research paper thumbnail of On Ramsey Numbers for Trees Versus Wheels of Five or Six Vertices

Graphs and Combinatorics, 2002

For given two graphs G dan H , the Ramsey number RðG; H Þ is the smallest positive integer n such... more For given two graphs G dan H , the Ramsey number RðG; H Þ is the smallest positive integer n such that every graph F of order n must contain G or the complement of F must contain H. In [12], the Ramsey numbers for the combination between a star S n and a wheel W m for m ¼ 4; 5 were shown, namely, RðS n ; W 4 Þ ¼ 2n À 1 for odd n and n ! 3, otherwise RðS n ; W 4 Þ ¼ 2n þ 1, and RðS n ; W 5 Þ ¼ 3n À 2 for n ! 3. In this paper, we shall study the Ramsey number RðG; W m Þ for G any tree T n. We show that if T n is not a star then the Ramsey number RðT n ; W 4 Þ ¼ 2n À 1 for n ! 4 and RðT n ; W 5 Þ ¼ 3n À 2 for n ! 3. We also list some open problems.

Research paper thumbnail of The Ramsey numbers of large cycles versus wheels

Discrete Mathematics, 2006

In this paper we show that the Ramsey number R(C n , W m) = 2n − 1 for even m and n 5m/2 − 1.

Research paper thumbnail of The Ramsey Numbers of Large cycles Versus Odd Wheels

Graphs and Combinatorics, 2008

Research paper thumbnail of The Ramsey number of paths with respect to wheels

Discrete Mathematics, 2005

For graphs G and H , the Ramsey number R(G, H) is the smallest positive integer n such that every... more For graphs G and H , the Ramsey number R(G, H) is the smallest positive integer n such that every graph F of order n contains G or the complement of F contains H. For the path P n and the wheel W m , it is proved that R(P n , W m) = 2n − 1 if m is even, m 4, and n (m/2)(m − 2), and R(P n , W m) = 3n − 2 if m is odd, m 5, and n (m − 1/2)(m − 3).

Research paper thumbnail of The Ramsey numbers of fans versus K 4

Research paper thumbnail of Total vertex irregular labeling of complete bipartite graphs

Research paper thumbnail of An Upper Bound for the Ramsey Number of a Cycle of Length Four Versus Wheels

Lecture Notes in Computer Science, 2005

For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that ... more For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that every graph F of n vertices satisfies the following property: either F contains G or the complement of F contains H. In this paper, we show that the Ramsey number R (C 4, ...

Research paper thumbnail of An upper bound for the ramsey number of a cycle of length four versus wheels

For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that ... more For given graphs G and H, the Ramsey numberR (G, H) is the smallest positive integer n such that every graph F of n vertices satisfies the following property: either F contains G or the complement of F contains H. In this paper, we show that the Ramsey number R (C 4, ...