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

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.

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.

@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},
     pages = {921--926},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {3},
     year = {1999},
     doi = {10.5802/aif.1699},
     zbl = {0920.05048},
     mrnumber = {2000d:05072},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1699/}
}
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
SP  - 921
EP  - 926
VL  - 49
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1699/
DO  - 10.5802/aif.1699
LA  - en
ID  - AIF_1999__49_3_921_0
ER  - 
%0 Journal Article
%A Jackson, Bill
%A Whitehead, Carol A.
%T Some remarks on Jaeger's dual-hamiltonian conjecture
%J Annales de l'Institut Fourier
%D 1999
%P 921-926
%V 49
%N 3
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1699/
%R 10.5802/aif.1699
%G en
%F AIF_1999__49_3_921_0
Jackson, Bill; Whitehead, Carol A. Some remarks on Jaeger's dual-hamiltonian conjecture. Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 921-926. doi : 10.5802/aif.1699. https://aif.centre-mersenne.org/articles/10.5802/aif.1699/

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

[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 | Zbl

[4] J.G. Oxley, Matroid Theory, Oxford Univ. Press, Oxford, 1992. | MR | Zbl

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

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

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

Cité par Sources :