Properly Coloured Cycles and Paths: Results and Open Problems
Discrete Mathematics
2008-05-31 v3 Data Structures and Algorithms
Abstract
In this paper, we consider a number of results and seven conjectures on properly edge-coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of transformations of an edge-coloured multigraph into an ordinary graph that allow us to check the existence PC cycles and PC -paths in and, if they exist, to find shortest ones among them. We raise a problem of finding the optimal transformation and consider a possible solution to the problem.
Cite
@article{arxiv.0805.3901,
title = {Properly Coloured Cycles and Paths: Results and Open Problems},
author = {Gregory Gutin and Eun Jung Kim},
journal= {arXiv preprint arXiv:0805.3901},
year = {2008}
}