On the equivalence between some local and global Chinese postman and traveling salesman graphs |
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Affiliation: | 1. Faculty of Commerce and Business Administration, University of British Columbia, 2053 Main Mall, Vancouver, British Columbia, BC V6T 1Z2, Canada;2. Center and Department of Econometrics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands |
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Abstract: | A connected graph G=(V,E), a vertex in V and a non-negative weight function defined on E can be used to induce Chinese postman and traveling salesman (cooperative) games. A graph G=(V,E) is said to be locally (respectively, globally) Chinese postman balanced (respectively, totally balanced, submodular) if for at least one vertex (respectively, for all vertices) in V and any non-negative weight function defined on E, the corresponding Chinese postman game is balanced (respectively, totally balanced, submodular). Local and global traveling salesman balanced (respectively, totally balanced, submodular) graphs are similarly defined.In this paper, we study the equivalence between local and global Chinese postman balanced (respectively, totally balanced, submodular) graphs, and between local and global traveling salesman submodular graphs. |
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