✦ LIBER ✦

Ramsey numbers for sets of small graphs

✍ Scribed by Holger Brandes; Heiko Harborth; Hans-Dietrich O.F. Gronau; Christian Schwahn

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 733 KB
Volume: 125
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90146-5

No coin nor oath required. For personal study only.

✦ Synopsis

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 graphs with at most four vertices, and in the diagonal case (m = n, Gi = Hi) for all pairs of graphs, one with at most four and the other with five vertices, so as for all sets of graphs with five vertices.

📜 SIMILAR VOLUMES

Diagonal Ramsey numbers for small graphs

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

Size Ramsey numbers for small-order grap

Size Ramsey numbers for small-order graphs

✍ R. J. Faudree; J. Sheehan 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 108 KB

A table of the size Ramsey number or the restricted size Rarnsey number for all pairs of graphs with at most four vertices and no isolated vertices is given. Let F, G, and H be finite, simple, and undirected graphs. The number of vertices and edges of a graph F are denoted byp(F) and q(F), respecti

On graphs with small Ramsey numbers

✍ A. V. Kostochka; V. Rödl 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 88 KB

## Abstract Let __R__(__G__) denote the minimum integer __N__ such that for every bicoloring of the edges of __K~N~__, at least one of the monochromatic subgraphs contains __G__ as a subgraph. We show that for every positive integer __d__ and each γ,0 < γ < 1, there exists __k__ = __k__(__d__,γ) su

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.

Irredundant ramsey numbers for graphs

✍ R. C. Brewster; E. J. Cockayne; C. M. Mynhardt 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 356 KB

Lower Ramsey numbers for graphs

✍ C.M. Mynhardt 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 380 KB

Let p(G) denote the smallest number of vertices in a maximal clique of the graph G, while i(G) (the independent domination number of G) denotes the smallest number of vertices in a maximal independent (i.e. independent dominating) set of G. For given integers 1 and m, the lower Ramsey number s(l, m)