Combinatorica

, Volume 13, Issue 2, pp 147–155

Cycles through specified vertices

  • Béla Bollobás
  • Graham Brightwell
Article

DOI: 10.1007/BF01303200

Cite this article as:
Bollobás, B. & Brightwell, G. Combinatorica (1993) 13: 147. doi:10.1007/BF01303200

Abstract

Recently, various authors have obtained results about the existence of long cycles in graphs with a given minimum degreed. We extend these results to the case where only some of the vertices are known to have degree at leastd, and we want to find a cycle through as many of these vertices as possible. IfG is a graph onn vertices andW is a set ofw vertices of degree at leastd, we prove that there is a cycle through at least\(\left\lceil {\frac{w}{{\left\lceil {{n \mathord{\left/ {\vphantom {n d}} \right. \kern-\nulldelimiterspace} d}} \right\rceil - 1}}} \right\rceil \) vertices ofW. We also find the extremal graphs for this property.

AMS subject classification code (1991)

05 C 38 

Copyright information

© Akadémiai Kiadò 1993

Authors and Affiliations

  • Béla Bollobás
    • 1
  • Graham Brightwell
    • 2
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of Cambridge 16CambridgeEngland
  2. 2.Dept. of Stat. and Math. SciencesLondon School of Economics and Political ScienceLondonEngland

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