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2004•Unpublished venueRequires access

The Ramsey numbers of large cycles versus small wheels

null Surahmat, Edy Tri Baskoro, Hajo J. Broersma

Open publisher page 13 citations

Abstract

For two given graphs G and H, the Ramsey number R(G;H) is the smallest positive integer N such that for every graph F of order N the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we determine the Ramsey number R(Cn;Wm) for m = 4 and m = 5. We show that R(Cn;W4) = 2n i 1 and R(Cn;W5) = 3n i 2 for n ¸ 5. For larger wheels it remains an open problem to determine R(Cn;Wm).

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What this paper is about

For two given graphs G and H, the Ramsey number R(G;H) is the smallest positive integer N such that for every graph F of order N the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we determine the Ramsey number R(Cn;Wm) for m = 4 and m = 5. We show that R(Cn;W4) = 2n i 1 and R(Cn;W5) = 3n i 2 for n ¸ 5. For larger wheels it remains an open problem to determine R(Cn;Wm).

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OpenAlex reports 13 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

For two given graphs G and H, the Ramsey number R(G;H) is the smallest positive integer N such that for every graph F of order N the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we determine the Ramsey number R(Cn;Wm) for m = 4 and m = 5. We show that R(Cn;W4) = 2n i 1 and R(Cn;W5) = 3n i 2 for n ¸ 5. For larger wheels it remains an open problem to determine R(Cn;Wm).

Key concepts: Ramsey's theorem, Combinatorics, Mathematics, Graph, Complement (music), Integer (computer science), Order (exchange), Induced subgraph

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