Geodesic
Chromatic uniqueness of graphs that are homeomorphic to $K_4$
Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 126-135

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We give a description of all chromatically unique graphs being homeomorphic to $K_4$ which can be derived from the complete graph with four vertices by sequential dividing only three edges. As a corollary we solve two problems stated in [4]. 
@article{DM_1995_7_4_a10,
     author = {V. L. Mironov},
     title = {Chromatic uniqueness of graphs that are homeomorphic to $K_4$},
     journal = {Diskretnaya Matematika},
     pages = {126--135},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_4_a10/}
}
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V. L. Mironov. Chromatic uniqueness of graphs that are homeomorphic to $K_4$. Diskretnaya Matematika, Tome 7 (1995) no. 4, pp. 126-135. http://geodesic.mathdoc.fr/item/DM_1995_7_4_a10/