Some remarks on Jaeger's dual-hamiltonian conjecture
Annales de l'Institut Fourier, Volume 49 (1999) no. 3, p. 921-926

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.

François Jaeger a conjecturé en 1974 que tout graphe G, cubique et cycliquement 4-connexe, est dual-hamiltonien, c’est-à-dire que l’on peut partitionner l’ensemble des sommets de G en deux sous-ensembles tels que chacun induit un arbre de G. Nous donnons plusieurs remarques sur cette conjecture.

@article{AIF_1999__49_3_921_0,
     author = {Jackson, Bill and Whitehead, Carol A.},
     title = {Some remarks on Jaeger's dual-hamiltonian conjecture},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {3},
     year = {1999},
     pages = {921-926},
     doi = {10.5802/aif.1699},
     zbl = {0920.05048},
     mrnumber = {2000d:05072},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1999__49_3_921_0}
}
Jackson, Bill; Whitehead, Carol A. Some remarks on Jaeger's dual-hamiltonian conjecture. Annales de l'Institut Fourier, Volume 49 (1999) no. 3, pp. 921-926. doi : 10.5802/aif.1699. http://www.numdam.org/item/AIF_1999__49_3_921_0/

[1] W.H. Cunningham and J. Edmonds, A combinatorial decomposition theory, Canadian J. Math., 32 (1980), 734-765. | MR 83c:05098 | Zbl 0442.05054

[2] B. Jackson and X. Yu, Hamilton cycles in plane triangulations, submitted.

[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. | MR 50 #9650 | Zbl 0307.05102

[4] J.G. Oxley, Matroid Theory, Oxford Univ. Press, Oxford, 1992. | MR 94d:05033 | Zbl 0784.05002

[5] C. Payan and M. Sakarovitch, Ensembles cycliquement stables et graphes cubiques, Cahiers du C.E.R.O., 17 (1975), 319-343. | MR 54 #5027 | Zbl 0314.05101

[6] W. T. Tutte, A theorem on planar graphs, Trans. Amer. Math. Soc., 82 (1956), 99-116. | MR 18,408e | Zbl 0070.18403

[7] H. Whitney, A theorem on graphs, Ann. of Math., 32 (1931), 378-390. | JFM 57.0727.03 | Zbl 0002.16101