Ramsey numbers upon vertex deletion Wigderson, Yuval Given a graph , its Ramsey number is the minimum so that every two‐coloring of contains a monochromatic copy of . It was conjectured by Conlon, Fox, and Sudakov that if one deletes a single vertex from , the Ramsey number can change by at most a constant factor. We disprove this conjecture, exhibiting an infinite family of graphs such that deleting a single vertex from each decreases the Ramsey number by a super‐constant factor. One consequence of this result is the following. There exists a family of graphs so that in any Ramsey coloring for (i.e., a coloring of a clique on vertices with no monochromatic copy of ), one of the color classes has density . Wiley 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22180 Wigderson Y. Ramsey numbers upon vertex deletion. <i>Journal of Graph Theory</i>. 2024;106(3):663-675. doi:<a href="https://doi.org/10.1002/jgt.23093">10.1002/jgt.23093</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.23093 info:eu-repo/semantics/altIdentifier/issn/0364-9024 info:eu-repo/semantics/altIdentifier/e-issn/1097-0118 info:eu-repo/semantics/openAccess