A perfect graph is critical, if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, a
On Deeply Critical Oriented Graphs
✍ Scribed by O.V. Borodin; D. Fon-Der-Flaass; A.V. Kostochka; A. Raspaud; E. Sopena
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 96 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0095-8956
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✦ Synopsis
For every positive integer k, we present an oriented graph G k such that deleting any vertex of G k decreases its oriented chromatic number by at least k and deleting any arc decreases the oriented chromatic number of G k by two.
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