Unique Fulkerson coloring of Petersen minor-free cubic graphs
β Scribed by Miao, Zhengke; Wang, Xiaofeng; Zhang, Cun-Quan
- Book ID
- 127037718
- Publisher
- Elsevier Science
- Year
- 2015
- Tongue
- English
- Weight
- 404 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0195-6698
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## Abstract A (1,2)βeulerian weight __w__ of a grph is hamiltonian if every faithful cover of __w__ is a set of two Hamilton circuits. Let __G__ be a 3βconnected cubic graph containing no subdivition of the Petersen graph. We prove that if __G__ admits a hamiltonian weight then __G__ is uniquely 3β
The following question was raised by Bruce Richter. Let G be a planar, 3-connected graph that is not a complete graph. Denoting by d(v) the degree of vertex v, is G L-list colorable for every list assignment L with |L(v)|=min{d(v), 6} for all v β V (G)? More generally, we ask for which pairs (r, k)