Geodesic
Systems of pair of $q$-distant representatives and graph colorings
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VII, Tome 293 (2002), pp. 5-25

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NP-completeness of a number of graph coloring problems connected with the frequency assignment problem is proved. For this purpose we introduce problems concerning systems of pairs of $q$-distant representatives (related to the well known problem about the system of distinct representatives, but being NP-complete for $q\ge2$), which turned out to be convenient for proving NP-completeness of various graph coloring problems. 
@article{ZNSL_2002_293_a0,
     author = {P. A. Golovach},
     title = {Systems of pair of $q$-distant representatives and graph colorings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--25},
     publisher = {mathdoc},
     volume = {293},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_293_a0/}
}
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P. A. Golovach. Systems of pair of $q$-distant representatives and graph colorings. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part VII, Tome 293 (2002), pp. 5-25. http://geodesic.mathdoc.fr/item/ZNSL_2002_293_a0/