Domination Number of Graphs Without Small Cycles
β Scribed by Xue-gang Chen; Moo Young Sohn
- Publisher
- Springer Japan
- Year
- 2011
- Tongue
- English
- Weight
- 167 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0911-0119
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## Abstract A proper vertex coloring of a graph __G__β=β(__V,E__) is acyclic if __G__ contains no bicolored cycle. A graph __G__ is acyclically __L__βlist colorable if for a given list assignment __L__β=β{__L__(__v__): __v__:βββ__V__}, there exists a proper acyclic coloringβΟβof __G__ such that Ο(_
The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that