Geodesic
On the number of boundary classes in the 3-colouring problem
Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 129-134

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The notion of a boundary class is a useful notion in the investigation of the complexity of extremal problems on graphs. One boundary class is known for the independent set problem and three boundary classes are known for the dominating set problem. In this paper it is proved that the set of boundary classes for the 3-colouring problem is infinite. 
@article{DM_2009_21_4_a10,
     author = {D. S. Malyshev},
     title = {On the number of boundary classes in the 3-colouring problem},
     journal = {Diskretnaya Matematika},
     pages = {129--134},
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     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2009_21_4_a10/}
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D. S. Malyshev. On the number of boundary classes in the 3-colouring problem. Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 129-134. http://geodesic.mathdoc.fr/item/DM_2009_21_4_a10/