Set G q ′ = G q − v if q ≡ 3 (mod 4) and G q ′ = G q − u 1 otherwise. Embed G q ′ into H and color the edges of G q ′ as red and write R = G q ′ .

For given graphs H1,...,Hk, k≥2, the k-color Ramsey number R(H1,...,Hk) is the smallest integer N such that every k-coloring of the edges of a complete ...

Physical Sciences and Engineering Mathematics Algebra and Number Theory. On three-color Ramsey numbers R(C4,K1,m,Pn). Article ID, Journal, Published Year, Pages ...

It gives some formulas and bounds for multicolor Ramsey numbers of several simple graphs, including those for R(Cm ,Cn ,Ck ) and R(Cm ,Cn ,Ck ,Cl ) for large m.

For given graphs H1,...,Hk, k≥2, the k-color Ramsey number R(H1,...,Hk) is the smallest integer N such that every k-coloring of the edges of a complete ...

Abstract. For graphs G1,G2,G3, the three-color Ramsey number R(G1, G2,G3) is the smallest integer n such that if we arbitrarily color the edges.

We study the bounds on 3-color Ramsey numbers R(H1,H2,H3), where Hi is an ... Considering F3=2K3∪2K2∪3K1 we obtain that S(2K3∪ K1,3∪2K2)=∅.

Mar 23, 2012 · We study the bounds on 3-color Ramsey numbers R(H1,H2,H3), where Hi is an isolate-free graph different from K2 with at most four vertices, ...

Determining the Ramsey number R(Cn, tWm) for any integers t ≥ 1, n ≥ 3 and m ≥ 4 in general is a challenging problem, but we conjecture that for any ... [ ...

[10] states that R(Pn, Pm) = m + ⌊n/2⌋ − 1 where m ≥ n ≥ 2. In 1975 ... R(Pn, K1,k1 , K1,k2 ,..., K1,kt , m1K2, m2K2,..., ms K2) = n + Λ. Lemma 3 ...