Reflexive coloring complexes for 3-edge-colorings of cubic graphs

Fiachra Knox; Bojan Mohar; Nathan Singer

doi:10.1016/j.disc.2021.112309

Reflexive coloring complexes for 3-edge-colorings of cubic graphs

Discrete Mathematics ◽

10.1016/j.disc.2021.112309 ◽

2021 ◽

Vol 344 (4) ◽

pp. 112309

Author(s):

Fiachra Knox ◽

Bojan Mohar ◽

Nathan Singer

Keyword(s):

Cubic Graphs ◽

Edge Colorings

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On Edge-Colorings of Cubic Graphs and a Formula of Roger Penrose

Graph Theory in Memory of G.A. Dirac - Annals of Discrete Mathematics ◽

10.1016/s0167-5060(08)70465-5 ◽

1988 ◽

pp. 267-279 ◽

Cited By ~ 3

Author(s):

F. Jaeger

Keyword(s):

Cubic Graphs ◽

Edge Colorings ◽

Roger Penrose

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Edge-colorings of cubic graphs with elements of point-transitive Steiner triple systems

Electronic Notes in Discrete Mathematics ◽

10.1016/j.endm.2007.07.005 ◽

2007 ◽

Vol 29 ◽

pp. 23-27 ◽

Cited By ~ 3

Author(s):

Daniel Král' ◽

Edita Máčajová ◽

Attila Pór ◽

Jean-Sébastien Sereni

Keyword(s):

Cubic Graphs ◽

Steiner Triple Systems ◽

Triple Systems ◽

Edge Colorings

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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 ◽

10.2478/v10006-012-0057-y ◽

2012 ◽

Vol 22 (3) ◽

pp. 765-778

Author(s):

Piotr Formanowicz ◽

Krzysztof Tanaś

Keyword(s):

Graph Theory ◽

Computer Networks ◽

Assignment Problem ◽

Perfect Matchings ◽

Cubic Graphs ◽

Cubic Graph ◽

Algorithmic Approach ◽

Edge Colorings ◽

Mathematical Properties

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.

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