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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1360,
author = {Andrey A. Dobrynin and Leonid S. Mel'nikov and Artem V. Pyatkin},
title = {Erd\H os regular graphs of even degree},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {269-279},
zbl = {1140.05027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1360}
}
Andrey A. Dobrynin; Leonid S. Mel'nikov; Artem V. Pyatkin. Erdős regular graphs of even degree. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 269-279. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1360/
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