Critical graphs, matchings and tours or a hierarchy of relaxations for the travelling salesman problem
- Cite this article as:
- Cornuéjols, G. & Pulleyblank, W.R. Combinatorica (1983) 3: 35. doi:10.1007/BF02579340
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If a graph isPk-critical, then it is alsoPl-critical for all largerl. In particular, for allk, Pk-critical graphs are hypomatchable.
A graphG=(V, E) has a perfectPk-matching if and only if for anyX⊆V the number ofPk-critical components inG[V - X] is not greater than |X|.
The problemPk can be solved in polynomial time provided we can recognizePk-critical graphs in polynomial time. In addition, we describe a procedure for recognizingPk-critical graphs which is polynomial in the size of the graph and exponential ink.