# An exact formula for all star-kipas Ramsey numbers

Binlong Li, Yanbo Zhang, Hajo Broersma

1 Citation (Scopus)

### Abstract

Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or the complement of G contains a G2. A complete bipartite graph K1,n is called a star. The kipas of order n+1 is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edge on the rim deleted. Whereas for star-wheel Ramsey numbers not all exact values are known to date, in contrast we determine all exact values of star-kipas Ramsey numbers.
Original language English 141-148 8 Graphs and combinatorics 33 1 https://doi.org/10.1007/s00373-016-1746-3 Published - Jan 2017

### Fingerprint

Ramsey number
Stars
Star
Wheel
Wheels
Graph in graph theory
Path
Complete Bipartite Graph
Joining
Complement
Integer
Vertex of a graph

### Keywords

• EWI-27594
• MSC-05C
• Wheel
• IR-104073
• Kipas
• Star
• Ramsey number

### Cite this

Li, Binlong ; Zhang, Yanbo ; Broersma, Hajo. / An exact formula for all star-kipas Ramsey numbers. In: Graphs and combinatorics. 2017 ; Vol. 33, No. 1. pp. 141-148.
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An exact formula for all star-kipas Ramsey numbers. / Li, Binlong; Zhang, Yanbo; Broersma, Hajo.

In: Graphs and combinatorics, Vol. 33, No. 1, 01.2017, p. 141-148.

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T1 - An exact formula for all star-kipas Ramsey numbers

AU - Li, Binlong

AU - Zhang, Yanbo

AU - Broersma, Hajo

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AB - Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or the complement of G contains a G2. A complete bipartite graph K1,n is called a star. The kipas of order n+1 is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edge on the rim deleted. Whereas for star-wheel Ramsey numbers not all exact values are known to date, in contrast we determine all exact values of star-kipas Ramsey numbers.

KW - EWI-27594

KW - MSC-05C

KW - Wheel

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