<abstract xmlns="http://www.w3.org/1999/xhtml"><p>It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.</p></abstract>

It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.

The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

Institute of Computing Science Pozna´n University of Technology, Piotrowo 2, 60-965 Pozna´n, Poland

Institute of Bioorganic Chemistry Polish Academy of Sciences, Z. Noskowskiego 12/14, 61-704 Pozna´n, Poland

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of...

The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

Published Online: Oct 06, 2012

Page range: 765 - 778

DOI: https://doi.org/10.2478/v10006-012-0057-y

Keywords
cubic graph, edge coloring, perfect matching, randomized algorithms, computer networks

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

Published Online: Oct 06, 2012

Page range: 765 - 778

DOI: https://doi.org/10.2478/v10006-012-0057-y

Keywordscubic graph, edge coloring, perfect matching, randomized algorithms, computer networks

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
cubic graph, edge coloring, perfect matching, randomized algorithms, computer networks