Counting the number of minimal paths in weighted coloured-edge graphs

Date
2011
Authors
Ensor, A
Lillo, F
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
arXiv, Cornell University
Abstract

A weighted coloured-edge graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such a graph paths are compared by their total weight in each colour, resulting in a Pareto set of minimal paths from one vertex to another. This paper will give a tight upper bound on the cardinality of a minimal set of paths for any weighted coloured-edge graph. Additionally, a bound is presented on the expected number of minimal paths in weighted bicoloured-edge graphs.

Description
Keywords
Graph theory , Minimal paths , Multimodal network , Transportation modes , Weighted coloured-edge graph
Source
arXiv:1112.3066 [math.CO]
DOI
Rights statement
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