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Maximum clique deleted from ramsey graphs of a graph and paths

Author

Listed:
  • Yan Li

    (University of Shanghai for Science and Technology)

  • Yusheng Li

    (Tongji University)

  • Ye Wang

    (Harbin Engineering University)

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.

Suggested Citation

  • Yan Li & Yusheng Li & Ye Wang, 2023. "Maximum clique deleted from ramsey graphs of a graph and paths," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-14, August.
  • Handle: RePEc:spr:jcomop:v:46:y:2023:i:1:d:10.1007_s10878-023-01068-9
    DOI: 10.1007/s10878-023-01068-9
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