Geodesic
Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 117-128 
V. A. Aksenov; O. V. Borodin; A. N. Glebov. Continuation of a $3$-coloring from a $7$-face onto a plane graph without $3$-cycles. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 117-128. http://geodesic.mathdoc.fr/item/SEMR_2004_1_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We characterize the $3$-colourings of a $7$-face in a plane graph without $3$-cycles that can be extended to a $3$-colouring of the whole graph.

[1] V. A. Aksenov, “O prodolzhenii 3-raskraski na ploskikh grafakh”, Diskretnyi analiz: Sb. nauch. tr., 26, In-t matematiki SO AN SSSR, Novosibirsk, 1974, 3–19

[2] V. A. Aksenov, O. V. Borodin, A. N. Glebov, “O prodolzhenii 3-raskraski s dvukh vershin v ploskom grafe bez 3-tsiklov”, Diskret. analiz i issled. operatsii, Ser. 1, 9:1 (2002), 3–26 | MR | Zbl

[3] V. A. Aksenov, O. V. Borodin, A. N. Glebov, “Prodolzhenie 3-raskraski s 6-grani na ploskii graf bez 3-tsiklov”, Diskret. analiz i issled. operatsii, Ser. 1, 10:3 (2003), 3–11 | MR | Zbl

[4] O. V. Borodin, “A new proof of Grünbaum's 3-color theorem”, Discrete Math., 169:1-3 (1997), 177–183 | DOI | MR | Zbl

[5] H. Grötzsch, “Ein Dreifarbensatz für dreikreisfreie Netze auf der Kugel”, Wiss. Ztschr. Martin-Luther-Univ. Halle-Wittenberg. Math.-Natur. R., 8:1 (1959), 109–120 | MR

[6] B. Grünbaum, Grötzsch's theorem on 3-coloring, Michigan Math. J., 10:3 (1963), 303–310 | DOI | MR | Zbl

[7] T. R. Jensen, C. Thomassen, “The color space of a graph”, J. Graph Theory, 34:3 (2000), 234–245 | 3.0.CO;2-G class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl