Ramsey Numbers for Trees of Small Maximum Degree

On Induced Ramsey Numbers for Graphs wit

On Induced Ramsey Numbers for Graphs with Bounded Maximum Degree

✍ Tomasz Łuczak; Vojtěch Rödl 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 435 KB

For graphs G and H we write G wÄ ind H if every 2-edge colouring of G yields an induced monochromatic copy of H. The induced Ramsey number for H is defined as r ind (H)=min[ |V(G)|: G wÄ ind H]. We show that for every d 1 there exists an absolute constant c d such that r ind (H n, d ) n cd for every

Small order graph-tree Ramsey numbers

✍ R.J. Faudree; C.C. Rousseau; R.H. Schelp 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 521 KB

With but a few exceptions, the Ramsey number r(G, T) is determined for all connected graphs G with at most five vertices and all trees T.

Local and Mean Ramsey Numbers for Trees

✍ B. Bollobás; A. Kostochka; R.H. Schelp 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 75 KB

In this note we find the local and mean k-Ramsey numbers for many trees for which the Erdo s So s tree conjecture holds. ## 2000 Academic Press The usual Ramsey number R(G, k) is the smallest positive integer n such that any coloring of the edges of K n by at most k colors contains a monochromatic

Diagonal Ramsey numbers for small graphs

✍ S. A. Burr 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 430 KB

The tripartite Ramsey number for trees

✍ Julia Böttcher; Jan Hladký; Diana Piguet 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 338 KB

## Abstract We prove that for all ε>0 there are α>0 and __n__~0~∈ℕ such that for all __n__⩾__n__~0~ the following holds. For any two‐coloring of the edges of __K__~__n, n, n__~ one color contains copies of all trees __T__ of order __t__⩽(3 − ε)__n__/2 and with maximum degree Δ(__T__)⩽__n__^α^. This

Ramsey numbers for sets of small graphs

✍ Holger Brandes; Heiko Harborth; Hans-Dietrich O.F. Gronau; Christian Schwahn 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 733 KB

The Ramsey number r=r(G1-GZ-...-G,,,,H1-Hz-...-Hn) denotes the smallest r such that every 2-coloring of the edges of the complete graph K, contains a subgraph Gi with all edges of one color, or a subgraph Hi with all edges of a second color. These Ramsey numbers are determined for all sets of graph