The Ramsey numbers of large cycles versus wheels

Three Results on Cycle-Wheel Ramsey Numbers

“…Chen et al [7] improved this result by reducing the lower bound on m from m ≥ 5n/2 − 1 to m ≥ 3n/2 + 1. To completely solve this case, Surahmat et al [21] proposed the following conjecture.…”

“…For large cycles versus odd wheels, Surahmat et al [21] proved that R(C m , W n ) = 2m − 1 for even n and m ≥ 5n/2 − 1. Chen et al [7] improved this result by reducing the lower bound on m from m ≥ 5n/2 − 1 to m ≥ 3n/2 + 1.…”

Combinatorial Theory of a Complete Graph K5

“…Noting that X(K n ) = n and S(K n ) = 1 for the pair F 1 and K n . By Burr's lower bound, R(F Ḡ , K n ) ≥ 2Ḡ(n-1) + 1.For n=3, Gupta [2] showed that ,R(F Ḡ , K 3 ) = 4Ḡ+1 for Ḡ ≥ 2 For n=4 , Surahmat [3] showed that , R(F Ḡ , K 4 ) = 6Ḡ+1 for Ḡ ≥ 3…”

Generalized Ramsey numbers for graphs

“…Moreover, F n is not F m -good for m ≤ n < m(m−1)/2. For Ramsey numbers of fans versus wheels of even order, Surahmat et al [129] proved that R(F n ,W 3 ) = 6n+1 for n ≥ 3. We generalize this result by showing that R(F n ,W m ) = 6n + 1 for odd m ≥ 3 and n ≥ (5m + 3)/4.…”

“…For large cycles versus odd wheels, Surahmat et al [130] proved the first nontrivial result, which is R(C m ,W n ) = 2m − 1 for even n and m ≥ 5n/2 − 1.…”