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3- and 4-critical graphs of small even order

✍ Scribed by G. Brinkmann; E. Steffen

Book ID
108316062
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
248 KB
Volume
169
Category
Article
ISSN
0012-365X

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A k-critical (multi-) graph G has maximum degree k, chromatic index χ (G) = k + 1, and χ (G -e) < k + 1 for each edge e of G. For each k ≥ 3, we construct k-critical (multi-) graphs with certain properties to obtain counterexamples to some well-known conjectures.

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## Abstract In 1960, Dirac posed the conjecture that __r__‐connected 4‐critical graphs exist for every __r__ ≥ 3. In 1989, Erdős conjectured that for every __r__ ≥ 3 there exist __r__‐regular 4‐critical graphs. In this paper, a technique of constructing __r__‐regular __r__‐connected vertex‐transiti