The existence of unavoidable sets of geographically good configurations
Appel, K. ; Haken, W.
Illinois J. Math., Tome 20 (1976) no. 4, p. 218-297 / Harvested from Project Euclid
A set of configurations is unavoidable if every planar map contains at least one element of the set. A configuration $\mathcal{L}$ is called geographically good if whenever a member country $M$ of $\mathcal{L}$ has any three neighbors $N_{1}$, $N_{2}$, $N_{3}$ which are not members of $\mathcal{L}$ then $N_{1}$, $N_{2}$, $N_{3}$ are consecutive (in some order) about $M$. ¶ The main result is a constructive proof that there exist finite unavoidable sets of geographically good configurations. This result is the first step in an investigation of an approach towards the Four Color Conjecture.
Publié le : 1976-06-15
Classification:  05C15,  57C35
@article{1256049898,
     author = {Appel, K. and Haken, W.},
     title = {The existence of unavoidable sets of geographically good configurations},
     journal = {Illinois J. Math.},
     volume = {20},
     number = {4},
     year = {1976},
     pages = { 218-297},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256049898}
}
Appel, K.; Haken, W. The existence of unavoidable sets of geographically good configurations. Illinois J. Math., Tome 20 (1976) no. 4, pp.  218-297. http://gdmltest.u-ga.fr/item/1256049898/