Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T14:44:43.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Ramsey Schur Numbers

Published online by Cambridge University Press:  15 February 2005

JENS-P. BODE ,
HANS-DIETRICH O. F. GRONAU  and
HEIKO HARBORTH
JENS-P. BODE
Affiliation:
Diskrete Mathematik, Technische Universität Braunschweig, 38023 Braunschweig, Germany (e-mail: [email protected], [email protected])
HANS-DIETRICH O. F. GRONAU
Affiliation:
Fachbereich Mathematik, Universität Rostock, Universitätsplatz 1, 18055 Rostock, Germany (e-mail: [email protected])
HEIKO HARBORTH
Affiliation:
Diskrete Mathematik, Technische Universität Braunschweig, 38023 Braunschweig, Germany (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

The Ramsey Schur number $RS(s,t)$ is the smallest $n$ such that every 2-colouring of the edges of $K_n$ with vertices $1,2,\ldots,n$ contains a green $K_s$ or there are vertices $x_1,x_2,\ldots,x_t$ fulfilling the equation $x_1+x_2+\cdots+x_{t-1}=x_t$ and all edges $(x_i,x_j)$ are red. We prove $RS(3,3)=11, RS(3,t)=t^2-3$ for $t\equiv1\ (\mbox{mod}\ 6)$ and $t=8$, and $RS(3,t)\geq t^2-3$.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 14 , Issue 1-2 , January 2005 , pp. 25 - 30
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)