Some remarks on Jaeger's dual-hamiltonian conjecture

Bill Jackson; Carol A. Whitehead

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 3, page 921-926
  • ISSN: 0373-0956

Abstract

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François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph G is dual hamiltonian, that is to say the vertices of G can be partitioned into two subsets such that each subset induces a tree in G . We shall make several remarks on this conjecture.

How to cite

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Jackson, Bill, and Whitehead, Carol A.. "Some remarks on Jaeger's dual-hamiltonian conjecture." Annales de l'institut Fourier 49.3 (1999): 921-926. <http://eudml.org/doc/75370>.

@article{Jackson1999,
abstract = {François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph $G$ is dual hamiltonian, that is to say the vertices of $G$ can be partitioned into two subsets such that each subset induces a tree in $G$. We shall make several remarks on this conjecture.},
author = {Jackson, Bill, Whitehead, Carol A.},
journal = {Annales de l'institut Fourier},
keywords = {cubic graph; dual-hamiltonian; hamiltonian cocircuit; partition; cycles},
language = {eng},
number = {3},
pages = {921-926},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some remarks on Jaeger's dual-hamiltonian conjecture},
url = {http://eudml.org/doc/75370},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Jackson, Bill
AU - Whitehead, Carol A.
TI - Some remarks on Jaeger's dual-hamiltonian conjecture
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 3
SP - 921
EP - 926
AB - François Jaeger conjectured in 1974 that every cyclically 4-connected cubic graph $G$ is dual hamiltonian, that is to say the vertices of $G$ can be partitioned into two subsets such that each subset induces a tree in $G$. We shall make several remarks on this conjecture.
LA - eng
KW - cubic graph; dual-hamiltonian; hamiltonian cocircuit; partition; cycles
UR - http://eudml.org/doc/75370
ER -

References

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  1. [1] W.H. CUNNINGHAM and J. EDMONDS, A combinatorial decomposition theory, Canadian J. Math., 32 (1980), 734-765. Zbl0442.05054MR83c:05098
  2. [2] B. JACKSON and X. YU, Hamilton cycles in plane triangulations, submitted. 
  3. [3] F. JAEGER, On vertex induced forests in cubic graphs, Proc. Fifth Southeastern Conf. on Combinatorics, Graph Theory and Computing, Utilitas Mathematica, Winnipeg (1974), 501-512. Zbl0307.05102MR50 #9650
  4. [4] J.G. OXLEY, Matroid Theory, Oxford Univ. Press, Oxford, 1992. Zbl0784.05002MR94d:05033
  5. [5] C. PAYAN and M. SAKAROVITCH, Ensembles cycliquement stables et graphes cubiques, Cahiers du C.E.R.O., 17 (1975), 319-343. Zbl0314.05101MR54 #5027
  6. [6] W. T. TUTTE, A theorem on planar graphs, Trans. Amer. Math. Soc., 82 (1956), 99-116. Zbl0070.18403MR18,408e
  7. [7] H. WHITNEY, A theorem on graphs, Ann. of Math., 32 (1931), 378-390. Zbl0002.16101JFM57.0727.03

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