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2012 | 22 | 3 | 765-778
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
22
Numer
3
Strony
765-778
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-03-27
poprawiono
2011-09-21
poprawiono
2012-01-16
Twórcy
  • Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland
  • Institute of Bioorganic Chemistry, Polish Academy of Sciences, Z. Noskowskiego 12/14, 61-704 Poznań, Poland
  • Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland
Bibliografia
  • Celmins, U.A. and Swart, E. (1979). The constructions of snarks, Research Report CORR, No. 18, Department of Combinatorics and Optimization, University of Waterloo, Waterloo.
  • Fan, G. and Raspaud, A. (1994). Fulkerson's conjecture and circuit covers, Journal of Combinatorial Theory, Series B 61(1): 133-138.
  • Fouquet, J.-L. and Vanherpe, J.-M. (2008). On Fan-Raspaud conjecture, CoRR-Computing Research Repository, abs/0809.4821.
  • Goldberg, M.K. (1981). Construction of class 2 graphs with maximum vertex degree 3, Journal of Combinatorial Theory, Series B 31(3): 282-291.
  • Holyer, I. (1981). The NP-completeness of edge coloring, SIAM Journal on Computing 10(4): 718-720.
  • Isaacs, R. (1975). Infinite families of nontrivial trivalent graphs which are not Tait colorable, American Mathematical Monthly 82(3): 221-239.
  • Kochol, M. (1996). Snarks without small cycles, Journal of Combinatorial Theory, Series B 67(1): 34-47.
  • Greenlaw, R. P. (1995). Cubic graphs, ACM Computing Surveys 27(4): 471-495.
  • Szekeres, G. (1973). Polyhedral decompositions of cubic graphs, Bulletin of the Australian Mathematical Society 8(3): 367-387.
  • Vizing, V. (1964). On an estimate of the chromatic class of a p-graph, Diskretnyj Analiz 3: 25-30.
  • Watkins, J. and Wilson, R. (1988). A survey of snarks, in Y. Alavi, G. Chartrand, O.R. Oellermann, and A.J. Schwenk (Eds.), Graph Theory, Combinatorics, and Applications, Wiley Interscience, New York, NY/Kalamazoo, MI.
  • Watkins, J. (1989). Snarks, Annals of the New York Academy of Sciences 576: 606-622.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-amcv22z3p765bwm
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