Geodesic
Small Ramsey Numbers for Books, Wheels, and Generalizations
Bernard Lidický1 ; Gweneth McKinley2 ; Florian Pfender3 ; Steven Van Overberghe4
1Iowa State University
2Center for Communications Research, La Jolla
3University of Colorado Denver
4Ghent University
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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We describe applications of a range of different computational methods to Ramsey numbers. We use flag algebras, local search, bottom-up generation, and enumeration of polycirculant graphs.These methods are applied to Ramsey numbers for books and wheels. We also initiate the study of generalized small Ramsey numbers. Let $GR(r,K_s,t)$ denote the minimum number of vertices $n$ such that any $r$-edge-coloring of $K_n$ has a copy of $K_s$ with at most $t$ colors. We establish over 20 new bounds including exact determination of the Ramsey numbers $R(W_5, W_7) = 15$, $R(W_5, W_9) = 18$, $R(B_2, B_8) = 21$, $R(B_3, B_7) = 20$, $GR(3,K_4,2) = 10$, and $GR(4,K_4,3) = 10$.
DOI : 10.37236/13577

Bernard Lidický  1   ; Gweneth McKinley  2   ; Florian Pfender  3   ; Steven Van Overberghe  4

1 Iowa State University
2 Center for Communications Research, La Jolla
3 University of Colorado Denver
4 Ghent University 
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     author = {Bernard Lidick\'y and Gweneth McKinley and Florian Pfender and Steven Van Overberghe},
     title = {Small {Ramsey} {Numbers} for {Books,} {Wheels,} and {Generalizations}},
     journal = {The electronic journal of combinatorics},
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Bernard Lidický; Gweneth McKinley; Florian Pfender; Steven Van Overberghe. Small Ramsey Numbers for Books, Wheels, and Generalizations. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13577

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