Clique tree inequalities and the symmetric travelling salesman problem
Mathematics of Operations Research
Triangle-Free Simple 2-Matchings in Subcubic Graphs (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Subclasses of solvable problems from classes of combinatorial optimization problems
Cybernetics and Systems Analysis
Constrained cycle covers in Halin graphs
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities. The central notion is that of a 3-edge cutset, namely, a set of 3 edges that, when removed, disconnects the graph. Conversely, our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem. The approach is illustrated on two examples, Halin graphs and prismatic graphs.