, Volume 3, Issue 1, pp 3552
First online:
Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
 G. CornuéjolsAffiliated withG.S.I.A., CarnegieMellon University
 , W. R. PulleyblankAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
 1.
If a graph isP _{ k }critical, then it is alsoP _{ l }critical for all largerl. In particular, for allk, P _{ k }critical graphs are hypomatchable.
 2.
A graphG=(V, E) has a perfectP _{ k }matching if and only if for anyX⊆V the number ofP _{ k }critical components inG[V  X] is not greater than X.
 3.
The problemP _{ k } can be solved in polynomial time provided we can recognizeP _{ k }critical graphs in polynomial time. In addition, we describe a procedure for recognizingP _{ k }critical graphs which is polynomial in the size of the graph and exponential ink.
AMS subject classification (1980)
05 C 38 Title
 Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
 Journal

Combinatorica
Volume 3, Issue 1 , pp 3552
 Cover Date
 198303
 DOI
 10.1007/BF02579340
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 05 C 38
 Industry Sectors
 Authors

 G. Cornuéjols ^{(1)}
 W. R. Pulleyblank ^{(2)}
 Author Affiliations

 1. G.S.I.A., CarnegieMellon University, 15213, Pittsburgh, PA, USA
 2. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada