Maximum clique deleted from ramsey graphs of a graph and paths

Yan Li, Yusheng Li and Ye Wang ()
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Yan Li: University of Shanghai for Science and Technology
Yusheng Li: Tongji University
Ye Wang: Harbin Engineering University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 1, No 2, 14 pages

Abstract: Abstract For graphs F, G and H, let $$F\rightarrow (G,H)$$ F → ( G , H ) signify that any red-blue edge coloring of F contains either a red G or a blue H, hence the Ramsey number R(G, H) is the smallest r such that $$K_r\rightarrow (G,H)$$ K r → ( G , H ) . Define $$K_t$$ K t as the surplus clique of (G, H) if $$K_r\setminus K_t\rightarrow (G,H)$$ K r \ K t → ( G , H ) , where $$r=R(G,H)$$ r = R ( G , H ) . For any graph G with $$s(G)=1$$ s ( G ) = 1 , we shall show that the maximum order of surplus clique of $$(G, P_n)$$ ( G , P n ) is exactly $$\lceil \frac{n}{2}\rceil $$ ⌈ n 2 ⌉ for large n.

Keywords: Ramsey number; Ramsey surplus clique; Path; Book (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01068-9

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