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Mathematical Programming

, Volume 5, Issue 1, pp 29–40 | Cite as

Edmonds polytopes and weakly hamiltonian graphs

  • Václav Chvátal
Article

Abstract

Jack Edmonds developed a new way of looking at extremal combinatorial problems and applied his technique with a great success to the problems of the maximal-weight degreeconstrained subgraphs. Professor C. St. J.A. Nash-Williams suggested to use Edmonds' approach in the context of hamiltonian graphs. In the present paper, we determine a new set of inequalities (the “comb inequalities”) which are satisfied by the characteristic functions of hamiltonian circuits but are not explicit in the straightforward integer programming formulation. A direct application of the linear programming duality theorem then leads to a new necessary condition for the existence of hamiltonian circuits; this condition appears to be stronger than the ones previously known. Relating linear programming to hamiltonian circuits, the present paper can also be seen as a continuation of the work of Dantzig, Fulkerson and Johnson on the traveling salesman problem.

Keywords

Characteristic Function Mathematical Method Integer Programming Direct Application Great Success 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    V. Chvátal, “Tough graphs and hamiltonian circuits”,Discrete Mathematics 5 (1973), to appear.Google Scholar
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Copyright information

© The Mathematical Programming Society 1973

Authors and Affiliations

  • Václav Chvátal
    • 1
  1. 1.Université de MontréalMontréalCanada

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