Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
- G. CornuéjolsAffiliated withG.S.I.A., Carnegie-Mellon University
- , W. R. PulleyblankAffiliated withDepartment of Combinatorics and Optimization, University of Waterloo
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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.
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|.
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
- Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
Volume 3, Issue 1 , pp 35-52
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