Geodesic
SAT polytopes are faces of polytopes of the traveling salesman problem
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 3, pp. 76-83

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Let $U=\{u_1,u_2,\dots,u_d\}$ be a set of boolean variables and $C$ be a boolean formula over $U$ in conjunctive normal form. Denote by $Y$ the set of characteristic vectors of all satisfying truth assignments for $C$. The SAT polytope, denoted by $S(U,C)$, is the convex hull of $Y$. Denote by $T_n$ the asymmetric traveling salesman polytope. We show that $S(U,C)$ is a face of $T_n$, for $n=|U|+2\operatorname{len}(C)$, and $\operatorname{len}(C)$ is the size of the formula $C$. Ill. 1, Bibliogr. 9.
Keywords: TSP polytope, SAT polytope
Mots-clés : face. 
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     author = {A. N. Maksimenko},
     title = {SAT polytopes are faces of polytopes of the traveling salesman problem},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {76--83},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2011_18_3_a6/}
}
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A. N. Maksimenko. SAT polytopes are faces of polytopes of the traveling salesman problem. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 3, pp. 76-83. http://geodesic.mathdoc.fr/item/DA_2011_18_3_a6/