article published yes Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 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 . Wiley2024 eng 0364-9024 1097-011810.1002/jgt.23093 1063663-675 yes Wigderson, Yuval. “Ramsey Numbers upon Vertex Deletion.” <i>Journal of Graph Theory</i>, vol. 106, no. 3, Wiley, 2024, pp. 663–75, doi:<a href="https://doi.org/10.1002/jgt.23093">10.1002/jgt.23093</a>. Wigderson, Yuval. “Ramsey Numbers upon Vertex Deletion.” <i>Journal of Graph Theory</i>. Wiley, 2024. <a href="https://doi.org/10.1002/jgt.23093">https://doi.org/10.1002/jgt.23093</a>. Y. Wigderson, “Ramsey numbers upon vertex deletion,” <i>Journal of Graph Theory</i>, vol. 106, no. 3. Wiley, pp. 663–675, 2024. Wigderson Y. 2024. Ramsey numbers upon vertex deletion. Journal of Graph Theory. 106(3), 663–675. 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> Wigderson, Y. (2024). Ramsey numbers upon vertex deletion. <i>Journal of Graph Theory</i>. Wiley. <a href="https://doi.org/10.1002/jgt.23093">https://doi.org/10.1002/jgt.23093</a> Y. Wigderson, Journal of Graph Theory 106 (2024) 663–675. 221802026-06-29T10:59:24Z2026-07-14T09:10:28Z