✦ LIBER ✦

Some connected ramsey numbers

✍ Scribed by R. J. Faudree; R. H. Schelp

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 489 KB
Volume: 2
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190020204

No coin nor oath required. For personal study only.

✦ Synopsis

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 co‐connected graph on at least n vertices, then A ⩽ G or B ⩽ Ḡ. If neither A or B contains a bridge, then it is known that r~c~(A, B) = r(A, B), where r(A, B) denotes the usual Ramsey number of A and B. In this paper r~c~(A, B) is calculated for some pairs (A, B) when r(A, B) is known and at least one of the graphs A or B has a bridge. In particular, r~c~(A, B) is calculated for A a path and B either a cycle, star, or complete graph, and for A a star and B a complete graph.

📜 SIMILAR VOLUMES

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

An upper bound for some ramsey numbers

✍ Andrew Thomason 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 307 KB 👁 1 views

New upper bounds for the ramsey numbers r ( k , I ) are obtained. In particular it is shown there is a constant A such that The ramsey number r(k, l ) is the smallest integer n, such that any coloring with red and blue of the edges of the complete graph K , of order n yields either a red K , subgra

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

New lower bounds of some diagonal Ramsey

New lower bounds of some diagonal Ramsey numbers

✍ Filip Guldan; Pavel Tomasta 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 122 KB 👁 1 views

A new construction of self-complementary graphs containing no Klo or K , is described. This construction gives the Ramsey number lower bounds r(10,lO) 2 458 and r(1 1,l 1 ) 2 542. The problem of determining the Ramsey numbers is known to be very difficult and so we are often satisfied with partial

All triangle-graph ramsey numbers for co

All triangle-graph ramsey numbers for connected graphs of order six

✍ R. J. Faudree; C. C. Rousseau; R. H. Schelp 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 356 KB

## Abstract The Ramsey numbers __r(K__~3′~ __G__) are determined for all connected graphs __G__ of order six.

Difference Ramsey Numbers and Issai Numb

Difference Ramsey Numbers and Issai Numbers

✍ Aaron Robertson 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 80 KB

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.