Threshold Ramsey multiplicity for odd cycles

David Conlon ^[3] ; Jacob Fox ^[1] ; Benny Sudakov ^[4] ; Fan Wei ^[2]
1. [1] Stanford University
  
  Stanford University
  
  Estados Unidos
2. [2] Princeton University
  
  Princeton University
  
  Estados Unidos
3. [3] Caltech, USA
4. [4] ETH, Switzerland
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Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 49-68
Idioma: inglés
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Resumen
- The Ramsey number r(H) of a graph H is the minimum n such that any two-coloring of the edges of the complete graph Kn contains a monochromatic copy of H. The threshold Ramsey multiplicity m(H) is then the minimum number of monochromatic copies of H taken over all two-edgecolorings of Kr(H) . The study of this concept was first proposed by Harary and Prins almost fifty years ago. In a companion paper, the authors have shown that there is a positive constant c such that the threshold Ramsey multiplicity for a path or even cycle with k vertices is at least (ck) k, which is tight up to the value of c. Here, using different methods, we show that the same result also holds for odd cycles with k vertices.