Postman tours and cycle covers
نویسنده
چکیده
Raspaud, A., Postman tours and cycle covers, Discrete Mathematics 111 (1993) 447-454. Let G be a bridgeless graph. We show that the length of a shortest postman tour is at most IF(G)1 + 1 k’(G)1 3 and that, if G is a minimally 2-edge connected graph, then the length is at most 21 V(G)l-2. We then deduce results concerning the length of a shortest cycle cover for graphs containing no subdivision of the Petersen graph.
منابع مشابه
Matching, Euler tours and the Chinese postman
The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more general b-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discu...
متن کاملCapacitated Windy Rural Postman Problem with Several Vehicles: A Hybrid Multi-Objective Simulated Annealing Algorithm
This paper presents the capacitated Windy Rural Postman Problem with several vehicles. For this problem, two objectives are considered. One of them is the minimization of the total cost of all vehicle routes expressed by the sum of the total traversing cost and another one is reduction of the maximum cost of vehicle route in order to find a set of equitable tours for the vehicles. Mathematical ...
متن کاملApproximation algorithms for metric tree cover and generalized tour and tree covers
Given a weighted undirected graph G = (V, E), a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of G. Arkin, Halldórsson and Hassin (1993) give approximation algorithms with factors respectively 3.5...
متن کاملNew facets and an enhanced branch-and-cut for the min-max K-vehicles windy rural postman problem
In this paper the Min-Max version of the Windy Rural Postman Problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been imp...
متن کاملApproximating the length of Chinese postman tours
This article develops simple and easy-to-use approximation formulae for the length of a Chinese Postman Problem (CPP) optimal tour on directed and undirected strongly connected planar graphs as a function of the number of nodes and the number of arcs for graphs whose nodes are randomly distributed on a unit square area. These approximations, obtained from a multi-linear regression analysis, all...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 111 شماره
صفحات -
تاریخ انتشار 1993