L. V. Quintas and F. Supnick. On some properties of shortest Hamiltonian circuits. American Mathematical Monthly, 72:977-980, 1965. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Convex-Hull-and-Line Traveling Salesman Problem: A.. - Deineko, Dal, Rote (1992) (Correct)
....minimal #or optimal# tour does not intersect itself . An intersection of a tour # is de#ned as a common point v 62 fp 1 ; p n g that is shared bytwo #or more# edges of #,or a common point w 2fp 1 ; p ng that is shared by three #or more# edges of #. A proof of Flood s result was given by Quintas and Supnick #1965#. An important consequence of this is the following. Assuming that not all cities lie on one line, an optimal tour has the property that the cities on the boundary of the convex hull of the cities are visited in their cyclic order. Note that the case where all cities lie on two parallel lines ....
Quintas, L. V., and F. Supnick #1965#, On some properties of shortest Hamiltonian circuits, American Mathematical Monthly 72, 977#980.
The Convex-Hull-and-Line Traveling Salesman Problem: A.. - Deineko, van Dal, Rote (1992) (Correct)
....optimal) tour does not intersect itself . An intersection of a tour is defined as a common point v 62 fp 1 ; p n g that is shared by two (or more) edges of , or a common point w 2 fp 1 ; p n g that is shared by three (or more) edges of . A proof of Flood s result was given by Quintas and Supnick [1965]. An important consequence of this is the following. Assuming that not all cities lie on one line, an optimal tour has the property that the cities on the boundary of the convex hull of the cities are visited in their cyclic order. Note that the case where all cities lie on two parallel lines ....
Quintas, L. V., and F. Supnick (1965), On some properties of shortest Hamiltonian circuits, American Mathematical Monthly 72, 977--980.
Well-Solvable Special Cases of the TSP: A Survey - Burkard, Deineko, van Dal.. (1995) (2 citations) (Correct)
....of the shortest tour. Flood s observation also implies the following statement. Lemma 3. 1 (Folklore) If all cities lie on the boundary of a convex polygon, the optimal tour is a cyclic walk along the boundary of the polygon (in clockwise or counterclockwise direction) 2 Quintas and Supnick [95] proved an analogous result for the case that the cities lie on a 2 sphere and consecutive cities are connected by minor geodesic arcs. In [94] and [96] Quintas and Supnick derive a complete solution for finding a longest traveling salesman tours in case of convex planar Euclidean point sets. ....
L.V. Quintas and F. Supnick, On some properties of shortest Hamiltonian circuits, American Mathematical Monthly 72, 1965, 977--980.
Three Easy Special Cases of the Euclidean Travelling.. - Deineko, Rudolf, van.. (1995) (Correct)
....the combinatorial structure of Supnick point sets is rather primitive: In case a Supnick set contains n 9 points, all these points must lie on a common straight line. Hence, Supnick point sets are trivial to recognize. This result was also mentioned without proof in a paper by Quintas and Supnick [11] in 1965. The proof combines the following two propositions. Proposition 6.1 Any non degenerate point set P in the Euclidean plane with jP j 9 contains a non degenerate subset P such that (i) jP j = 5 and (ii) P is a convex set. Proposition 6.2 Let C be a 5 Theta 5 Supnick matrix. ....
L.V. Quintas and F. Supnick, On some properties of shortest Hamiltonian circuits, American Mathematical Monthly 72, 1965, 977--980.
On Polyhedra Induced by Point Sets in Space - Hurtado, Toussaint, Trias (2003) (Correct)
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L. V. Quintas and F. Supnick. On some properties of shortest Hamiltonian circuits. American Mathematical Monthly, 72:977-980, 1965.
Simple Polygons with an Infinite Sequence of Deflations - Fevens, Hernandez, Mesa.. (Correct)
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L. V. Quintas and F. Supnick. On some properties of shortest hamiltonian circuits. American Mathematical Monthly, 72, 1965.
On Polyhedra Induced by Point Sets in Space - Hurtado, Toussaint, Trias (Correct)
No context found.
L. V. Quintas and F. Supnick. On some properties of shortest Hamiltonian circuits. American Mathematical Monthly, 72:977-980, 1965.
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