Properly Coloured Cycles and Paths: Results and Open Problems

Authors:
Gregory Gutin;Eun Jung Kim
Affiliations:
Department of Computer Science, University of London, Egham, Surrey, UK TW20 0EX;Department of Computer Science, University of London, Egham, Surrey, UK TW20 0EX
Venue:
Graph Theory, Computational Intelligence and Thought
Year:
2009

Citing 12
Cited 1

Data structures and network algorithms

Data structures and network algorithms
Hamiltonian circuits determining the order of chromosomes

Discrete Applied Mathematics
Alternating cycles and paths in edge-coloured multigraphs: a survey

Proceedings of an international symposium on Graphs and combinatorics
A note on alternating cycles in edge-coloured graphs

Journal of Combinatorial Theory Series B
Properly colored Hamilton cycles in edge-colored complete graphs

Random Structures & Algorithms
Alternating cycles and trails in 2-edge-coloured complete multigraphs

Discrete Mathematics
Data structures for weighted matching and nearest common ancestors with linking

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Finding paths in graphs avoiding forbidden transitions

Discrete Applied Mathematics
On the Complexity of Some Hamiltonian and Eulerian Problems in Edge-Colored Complete Graphs

ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Characterization of edge-colored complete graphs with properly colored Hamilton paths

Journal of Graph Theory
Digraphs: Theory, Algorithms and Applications

Digraphs: Theory, Algorithms and Applications
Paths and trails in edge-colored graphs

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics

Complexity of paths, trails and circuits in arc-colored digraphs

TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we consider a number of results and six conjectures on properly 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 G into an ordinary graph that allow us to check the existence of PC cycles and PC (s ,t )-paths in G 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.