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For k given graphs H 1 , ... , H k , k ≥ 2 , the k -color Ramsey number, denoted by R (H 1 , ... , H k) , is the smallest integer N such that if we arbitrarily color the edges of a complete graph of order N with k colors, then it always contains a monochromatic copy of H i colored with i , for some 1 ≤ i ≤ k. Let C m be a cycle of length m , K 1 , n a star of order n + 1 and W n a wheel of order n + 1. In this paper, by using algebraic and probabilistic methods, we first give two lower bounds for (k + 1) -color Ramsey number R (C 4 , ... , C 4 , K 1 , n) for some special n , which shows the upper bound due to Zhang et al. (2019) is tight in some sense, and then establish a general lower bound for R (C 4 , ... , C 4 , K 1 , n) in terms of n and k , which extends the classical result of Burr et al. (1989). Moreover, we show that R (C 4 , ... , C 4 , K 1 , n) = R (C 4 , ... , C 4 , W n) for sufficiently large n. [ABSTRACT FROM AUTHOR]

For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Sn denote a star of order n and Wm a wheel of order m+1. This paper shows that R(Sn,W6)=2n+1 for n≥3 and R(Sn,Wm)=3n-2 for m odd and n≥m-1≥2. [Copyright &y& Elsevier]

Let Tn denote a tree of order n and Wm a wheel of order m + 1. In a previous paper, we evaluated the Ramsey number R(Tn, Wm) in the cases where Tn is the star of order n and m = 6 or m is odd and n ≥ m - 1 ≥ 2. In this paper, we determine R(Tn, W6) in the case where the maximum degree of Tn is at least n - 3. Our results show that a recent conjecture of Baskoro et al. is false. [Copyright &y& Elsevier]

Abstract: For two given graphs and , the Ramsey number is the smallest integer such that for any graph of order , either contains or the complement of contains . Let denote a cycle of order and a wheel of order . In this paper, we show that for odd, and , which was conjectured by Surahmat, Baskoro and Tomescu. [Copyright &y& Elsevier]

Abstract: For two given graphs and , the Ramsey number is the smallest integer n such that for any graph G of order n, either G contains or the complement of G contains . Let denote a path of order n and a wheel of order . In this paper, we show that for m even and and for m odd and . [Copyright &y& Elsevier]

Abstract: For two given graphs and , the Ramsey number is the smallest integer such that for any graph of order , either contains or the complement of contains . Let denote a cycle of order and a wheel of order . It is conjectured by Surahmat, E.T. Baskoro and I. Tomescu that for even , and . In this paper, we confirm the conjecture for . [Copyright &y& Elsevier]

For graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest integer N such that, for any graph G of order N , G contains G 1 as a subgraph or the complement of G contains G 2 as a subgraph. Let T n denote a tree of order n , W n a wheel of order n + 1 and F n a fan of order 2 n + 1 . We establish Ramsey numbers for fans and trees versus wheels of even order, thereby extending several known results. In particular, we prove that R ( F n , W m ) = 6 n + 1 for odd m ≥ 3 and n ≥ ( 5 m + 3 ) / 4 , and that R ( T n , W m ) = 3 n − 2 for odd m ≥ 3 and n ≥ m − 2 , and T n being a tree for which the Erdős–Sós Conjecture holds. [ABSTRACT FROM AUTHOR]

Abstract: Given two graphs and , the Ramsey number is the smallest integer such that for any graph of order , either contains or its complement contains . Let denote a cycle of order and a wheel of order . In this paper, it is shown that for odd, and , and for odd and . [Copyright &y& Elsevier]