In this thesis, we deal with rainbow colorings of graphs. We engage not with the
rainbow connection number but with counting of rainbow colorings in graphs with k
colors. We introduce the rainbow polynomial and prove some results for some special graph classes. Furthermore, we obtain bounds for the rainbow polynomial.
In addition, we define some edge colorings related to the rainbow coloring, like the
s-rainbow coloring and the 2-rainbow coloring. For this edge colorings, polynomials
are defined and we prove some basic properties for this polynomials and present some formulas for the calculation in special graph classes. In addition, we consider in this thesis counting problems related to the rainbow coloring like rainbow pairs and rainbow dependent sets. We introduce polynomials for this counting problems and present some general properties and formulas for special graph classes.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:33584 |
| Date | 05 April 2019 |
| Creators | Kischnick, Sara |
| Contributors | Tittmann, Peter, Schiermeyer, Ingo, TU Bergakademie Freiberg, Hochschule Mittweida |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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