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Corrections to “The Ramsey Numbers for a Quadrilateral vs. All Graphs on Six Vertices”

Luis Boza1
1Department of Applied Mathematics I, University of Seville, Seville, 41012, Spain

Abstract

The values of the Ramsey numbers \( R(C_4, H) \), for any graph \( H \) on 6 vertices, are shown in [3]. An erratum is corrected in [4,6], giving \( R(C_4, K_{3,3}) = 11 \).

In this paper, we correct three other errata of [3], proving that \( R(C_4, K_1 + (K_{2,3} – e)) = 9 \), \( R(C_4, \overline{K_3 \cup P_3}) = 11 \), and \( R(C_4, \overline{2P_3}) = 11 \), instead of 10.

Keywords: Graph Theory, extremal problem, Ramsey number, small graph, cycle.