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

Piotr Formanowicz; Krzysztof Tanaś

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 3, page 765-778
- ISSN: 1641-876X

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topPiotr Formanowicz, and Krzysztof Tanaś. "The Fan-Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 765-778. <http://eudml.org/doc/244056>.

@article{PiotrFormanowicz2012,

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.},

author = {Piotr Formanowicz, Krzysztof Tanaś},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {cubic graph; edge coloring; perfect matching; randomized algorithms; computer networks},

language = {eng},

number = {3},

pages = {765-778},

title = {The Fan-Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks},

url = {http://eudml.org/doc/244056},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Piotr Formanowicz

AU - Krzysztof Tanaś

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 3

SP - 765

EP - 778

AB - 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.

LA - eng

KW - cubic graph; edge coloring; perfect matching; randomized algorithms; computer networks

UR - http://eudml.org/doc/244056

ER -

## References

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