A graph G = (V, E ) with vertex set V and edge set E is called (a, b)-choosable ( a 2 2b) if for any collection {L(w)lv E V} of sets L ( v ) of cardinality a there exists a collection Giving a partial solution to a problem raised by Erdos, Rubin, and Taylor in 1979, we prove that every (2. 1)-choos
Every Planar Graph Is 5-Choosable
β Scribed by C. Thomassen
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 56 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
We prove the statement of the title, which was conjectured in 1975 by V. G. Vizing and, independently, in 1979 by P. ErdΓΆs, A. L. Rubin, and H. Taylor. (i) 1994 Academic Press, Inc.
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The conjecture on acyclic 5-choosability of planar graphs [Borodin et al., 2002] as yet has been verified only for several restricted classes of graphs. None of these classes allows 4-cycles. We prove that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cy
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