Bipartite Ramsey theorems for multiple copies of K2,2

Michael A. Henning; Ortrud R. Oellermann

Bipartite Ramsey theorems for multiple copies of K_2,2

Michael A. Henning, Ortrud R. Oellermann

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

For bipartite graphs G₁ , G₂ , ... ,G_k , the bipartite Ramsey number b(G₁ , G₂ , ... , G_k) is the least positive integer b so that any colouring of the edges of K_b,b with k colours will result in a copy of G_i in the ith colour for some i. When G_i = G for all i, we write b_k(G) = 6(G₁ , G₂ , ... , G_k), and we write b(G) = b₂(G). For all integers n ≥ 2, we show that 6(nK2,2) = 4n - 1; that is, any 2-colouring of the edges of K_4n-1,4n-1 contains a monochromatic nK_2,2.

Original language	English
Pages (from-to)	13-23
Number of pages	11
Journal	Utilitas Mathematica
Volume	54
Publication status	Published - Nov 1998
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Cite this

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title = "Bipartite Ramsey theorems for multiple copies of K2,2",

abstract = "For bipartite graphs G1 , G2 , ... ,Gk , the bipartite Ramsey number b(G1 , G2 , ... , Gk) is the least positive integer b so that any colouring of the edges of Kb,b with k colours will result in a copy of Gi in the ith colour for some i. When Gi = G for all i, we write bk(G) = 6(G1 , G2 , ... , Gk), and we write b(G) = b2(G). For all integers n ≥ 2, we show that 6(nK2,2) = 4n - 1; that is, any 2-colouring of the edges of K4n-1,4n-1 contains a monochromatic nK2,2.",

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AU - Henning, Michael A.

AU - Oellermann, Ortrud R.

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N2 - For bipartite graphs G1 , G2 , ... ,Gk , the bipartite Ramsey number b(G1 , G2 , ... , Gk) is the least positive integer b so that any colouring of the edges of Kb,b with k colours will result in a copy of Gi in the ith colour for some i. When Gi = G for all i, we write bk(G) = 6(G1 , G2 , ... , Gk), and we write b(G) = b2(G). For all integers n ≥ 2, we show that 6(nK2,2) = 4n - 1; that is, any 2-colouring of the edges of K4n-1,4n-1 contains a monochromatic nK2,2.

AB - For bipartite graphs G1 , G2 , ... ,Gk , the bipartite Ramsey number b(G1 , G2 , ... , Gk) is the least positive integer b so that any colouring of the edges of Kb,b with k colours will result in a copy of Gi in the ith colour for some i. When Gi = G for all i, we write bk(G) = 6(G1 , G2 , ... , Gk), and we write b(G) = b2(G). For all integers n ≥ 2, we show that 6(nK2,2) = 4n - 1; that is, any 2-colouring of the edges of K4n-1,4n-1 contains a monochromatic nK2,2.

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M3 - Article

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SN - 0315-3681

VL - 54

SP - 13

EP - 23

JO - Utilitas Mathematica

JF - Utilitas Mathematica

ER -

Bipartite Ramsey theorems for multiple copies of K_2,2

Abstract

ASJC Scopus subject areas

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