𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Difference Ramsey Numbers and Issai Numbers

✍ Scribed by Aaron Robertson

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
80 KB
Volume
25
Category
Article
ISSN
0196-8858

No coin nor oath required. For personal study only.

✦ Synopsis

We present a recursive algorithm for finding good lower bounds for the classical Ramsey numbers. Using notions from this algorithm we then give some results for generalized Schur numbers, which we call Issai numbers.

📜 SIMILAR VOLUMES

Planar Ramsey Numbers
Planar Ramsey Numbers
✍ R. Steinberg; C.A. Tovey 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 240 KB

The planar Ramsey number \(P R(k, l)(k, l \geqslant 2)\) is the smallest integer \(n\) such that any planar graph on \(n\) vertices contains either a complete graph on \(k\) vertices or an independent set of size \(l\). We find exact values of \(P R(k, l)\) for all \(k\) and \(l\). Included is a pro

Some small ramsey numbers
Some small ramsey numbers
✍ M. Clancy 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 82 KB

## Abstract In previous work, the Ramsey numbers have been evaluated for all pairs of graphs with at most four points. In the present note, Ramsey numbers are tabulated for pairs __F__~1~, __F__~2~ of graphs where __F__~1~ has at most four points and __F__~2~ has exactly five points. Exact results

Some connected ramsey numbers
Some connected ramsey numbers
✍ R. J. Faudree; R. H. Schelp 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 489 KB

## Abstract A graph __G__ is co‐connected if both __G__ and its complement __Ḡ__ are connected and nontrivial. For two graphs __A__ and __B__, the connected Ramsey number __r__~c~(__A, B__) is the smallest integer __n__ such that there exists a co‐connected graph of order __n__, and if __G__ is a c

Mean Ramsey–Turán numbers
Mean Ramsey–Turán numbers
✍ Raphael Yuster 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 124 KB

## Abstract A ρ‐mean coloring of a graph is a coloring of the edges such that the average number of colors incident with each vertex is at most ρ. For a graph __H__ and for ρ ≥ 1, the __mean Ramsey–Turán number RT__(__n, H,ρ − mean__) is the maximum number of edges a ρ‐__mean__ colored graph with _

On Regressive Ramsey Numbers
On Regressive Ramsey Numbers
✍ Peter Floodstrand Blanchard 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 111 KB

## for my mentors don bonar and gerald thompson We prove the following relation between regressive and classical Ramsey numbers ¼ 8; R 4 reg ð6Þ ¼ 15; and R 5 reg ð7Þ536: We prove that R 2 xþk ð4Þ42 kþ1 ð3 þ kÞ À ðk þ 1Þ; and use this to compute R 2 reg ð5Þ ¼ 15: Finally, we provide the bounds 19