On some path-critical Ramsey numbers

Ye Wang () and Yanyan Song ()
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Ye Wang: Harbin Engineering University
Yanyan Song: Harbin Engineering University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 5, No 16, 9 pages

Abstract: Abstract For graphs G and H, the Ramsey number R(G, H) is the smallest r such that any red-blue edge coloring of $$K_r$$ K r contains a red G or a blue H. The path-critical Ramsey number $$R_{\pi }(G,H)$$ R π ( G , H ) is the largest n such that any red-blue edge coloring of $$K_r \setminus P_{n}$$ K r \ P n contains a red G or a blue H, where $$r=R(G,H)$$ r = R ( G , H ) and $$P_{n}$$ P n is a path of order n. In this note, we show a general upper bound for $$R_{\pi }(G,H)$$ R π ( G , H ) , and determine the exact values for some cases of $$R_{\pi }(G,H)$$ R π ( G , H ) .

Keywords: Path-critical Ramsey number; Ramsey goodness; Path (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01312-4

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