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Bounds on Ramsey Numbers of Certain Complete Bipartite Graphs

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Abstract

Bounds on the Ramsey number r(Kl,m,Kl,n), where we may assume l ≤ m ≤ n, are determined for 3 ≤ l ≤ 5 and m ≈ n. Particularly, for m = n the general upper bound on r(Kl,n, Kl,n) due to Chung and Graham is improved for those l. Moreover, the behavior of r(K3,m, K3,n) is studied for m fixed and n sufficiently large.

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Authors and Affiliations

  1. Technische Universität Braunschweig Abteilung Diskrete Mathematik, Germany

    Roland Lortz & Ingrid Mengersen

  2. Volkswagen AG Informationssysteme Fahrzeugplanung, Brieffach 1830, 38436, Wolfsburg, Germany

    Roland Lortz

  3. Moorhüttenweg 2d, 38104, Braunschweig, Germany

    Ingrid Mengersen

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  1. Roland Lortz
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  2. Ingrid Mengersen
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Correspondence to Roland Lortz.

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Lortz, R., Mengersen, I. Bounds on Ramsey Numbers of Certain Complete Bipartite Graphs. Results. Math. 41, 140–149 (2002). https://doi.org/10.1007/BF03322761

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