On normal partitions in cubic graphs

Jean-Luc Fouquet; Jean-Marie Vanherpe

Discussiones Mathematicae Graph Theory (2009)

  • Volume: 29, Issue: 2, page 293-312
  • ISSN: 2083-5892

Abstract

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A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.

How to cite

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Jean-Luc Fouquet, and Jean-Marie Vanherpe. "On normal partitions in cubic graphs." Discussiones Mathematicae Graph Theory 29.2 (2009): 293-312. <http://eudml.org/doc/270604>.

@article{Jean2009,
abstract = {A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.},
author = {Jean-Luc Fouquet, Jean-Marie Vanherpe},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cubic graph; edge-partition},
language = {eng},
number = {2},
pages = {293-312},
title = {On normal partitions in cubic graphs},
url = {http://eudml.org/doc/270604},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Jean-Luc Fouquet
AU - Jean-Marie Vanherpe
TI - On normal partitions in cubic graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2009
VL - 29
IS - 2
SP - 293
EP - 312
AB - A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.
LA - eng
KW - cubic graph; edge-partition
UR - http://eudml.org/doc/270604
ER -

References

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  1. [1] J.A. Bondy, Basic graph theory: Paths and circuits, in: M. Grötschel, R.L. Graham and L. Lovász, eds, Handbook of Combinatorics, vol. 1, pages 3-112 (Elsevier, North-Holland, 1995). Zbl0849.05044
  2. [2] A. Bouchet and J.L. Fouquet, Trois types de décompositions d'un graphe chaînes, Annals of Discrete Math. 17 (1983) 131-141. Zbl0537.05052
  3. [3] G. Fan and A. Raspaud, Fulkerson's conjecture and circuit covers, J. Combin. Theory (B) 61 (1994) 133-138, doi: 10.1006/jctb.1994.1039. Zbl0811.05053
  4. [4] L. Goddyn, Cones, lattices and Hilbert base of circuits and perfect matching, in: N. Robertson and P. Seymour, eds, Graph Structure Theory, Contemporary Mathematics Volume 147, pages 419-439 (American Mathematical Society, 1993), doi: 10.1090/conm/147/01189. 
  5. [5] R. Halin, A theorem on n-connected graphs, J. Combin. Theory (1969) 150-154. Zbl0172.25803
  6. [6] J.M. Vanherpe, J.L. Fouquet, H. Thuillier and A.P. Wojda, On odd and semi-odd linear partitions of cubic graphs, preprint, 2006. Zbl1193.05130
  7. [7] D. König, Über Graphen und ihre Anwendung auf Determinantentheorie und Mengenlehre, Math. Ann. 77 (1916) 453-465, doi: 10.1007/BF01456961. 
  8. [8] A. Kotzig, Moves without forbidden transitions, Mat.-Fyz. Casopis 18 (1968) 76-80, MR 39#4038. Zbl0155.31901
  9. [9] H. Li, Perfect path double covers in every simple graphs, J. Graph. Theory 14 (1990) 645-650, MR 91h#05052. Zbl0725.05054
  10. [10] P. Seymour, On multi-colourings of cubic graphs and conjectures of Fulkerson and Tutte, Proc. London Math. Soc. (3) 38 (1979) 423-460, doi: 10.1112/plms/s3-38.3.423. Zbl0411.05037

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