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The path, the wheelbarrow, and the bicycle inequalities have been shown by Cornuéjols, Fonlupt, and Naddef to be facetdefining for the graphical relaxation of STSP n , the polytope of the symmetric traveling salesman problem on an n-node complete graph. We show that these inequalities, and some generalizations of them, define facets also for STSP n . In conclusion, we characterize a large family of facet-defining inequalities for STSP n that include, as special cases, most of the inequalitiesdoi:10.1287/moor.1060.0244 fatcat:dmyqo4rqqrfm5n627cttiauldi