Turán Colourings in Off-Diagonal Ramsey Multiplicity
The Ramsey multiplicity constant of a graph $H$ is the limit as $n$ tends to infinity of the minimum density of monochromatic labeled copies of $H$ in a $2$-edge colouring of $K_n$. Fox and Wigderson recently identified a large family of graphs whose Ramsey multiplicity constants are attained by seq...
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| Published in | The Electronic journal of combinatorics Vol. 32; no. 2 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
25.04.2025
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| Online Access | Get full text |
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| Summary: | The Ramsey multiplicity constant of a graph $H$ is the limit as $n$ tends to infinity of the minimum density of monochromatic labeled copies of $H$ in a $2$-edge colouring of $K_n$. Fox and Wigderson recently identified a large family of graphs whose Ramsey multiplicity constants are attained by sequences of "Turán colourings"; i.e. colourings in which one of the colour classes forms the edge set of a balanced complete multipartite graph. Each graph in their family comes from taking a connected non-3-colourable graph with a critical edge and adding many pendant edges. We extend their result to an off-diagonal variant of the Ramsey multiplicity constant which involves minimizing a weighted sum of red copies of one graph and blue copies of another. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/12751 |