Geodesic
Erdős regular graphs of even degree
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 269-279

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In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.
Keywords: vertex coloring, 4-critical graph, circulant, regular graph, vertex connectivity 
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     title = {Erd\H{o}s regular graphs of even degree},
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Dobrynin, Andrey; Mel'nikov, Leonid; Pyatkin, Artem. Erdős regular graphs of even degree. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a4/