Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T22:30:32.246Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on the Number of Complete and Empty Subgraphs

Published online by Cambridge University Press:  01 June 1998

RICHARD H. SCHELP  and
ANDREW THOMASON
RICHARD H. SCHELP
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA (e-mail: schelpr@msci.memphis.edu)
ANDREW THOMASON
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA (e-mail: schelpr@msci.memphis.edu) Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, UK (e-mail: A.G.Thomason@dpmms.cam.ac.uk)
Get access Rights & Permissions [Opens in a new window]

Abstract

Let kp(G) denote the number of complete subgraphs of order p in the graph G. Bollobás proved that any real linear combination of the form [sum ]apkp(G) attains its maximum on a complete multipartite graph. We show that the same is true for a linear combination of the form [sum ]apkp(G) +bpkp(G¯), provided bp[ges ]0 for every p.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 2 , June 1998 , pp. 217 - 219
Copyright
1998 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.)