Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-23T08:11:50.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth

Published online by Cambridge University Press:  01 December 1998

THOMAS EMDEN-WEINERT ,
STEFAN HOUGARDY  and
BERND KREUTER
THOMAS EMDEN-WEINERT
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany (e-mail: TEmdenWe@vss.comhougardy@informatik.hu-berlin.debernd.kreuter@sap-ag.de)
STEFAN HOUGARDY
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany (e-mail: TEmdenWe@vss.comhougardy@informatik.hu-berlin.debernd.kreuter@sap-ag.de)
BERND KREUTER
Affiliation:
Institut für Informatik, Humboldt-Universität zu Berlin, 10099 Berlin, Germany (e-mail: TEmdenWe@vss.comhougardy@informatik.hu-berlin.debernd.kreuter@sap-ag.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

For any integer k, we prove the existence of a uniquely k-colourable graph of girth at least g on at most k12(g+1) vertices whose maximal degree is at most 5k13. From this we deduce that, unless NP=RP, no polynomial time algorithm for k-Colourability on graphs G of girth g(G)[ges ]log[mid ]G[mid ]/13logk and maximum degree Δ(G)[les ]6k13 can exist. We also study several related problems.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 4 , December 1998 , pp. 375 - 386
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.)