On chordal digraphs and semi-strict chordal digraphs
Chordal graphs are an important class of perfect graphs. The beautiful theory surrounding their study varies from natural applications to elegant characterizations in terms of forbidden subgraphs, subtree representations, vertex orderings, and to linear time recognition algorithms. Haskins and Ro...
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| Format: | Others |
| Language: | English en |
| Published: |
2019
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| Online Access: | http://hdl.handle.net/1828/11083 |
| Summary: | Chordal graphs are an important class of perfect graphs. The beautiful theory
surrounding their study varies from natural applications to elegant characterizations
in terms of forbidden subgraphs, subtree representations, vertex orderings, and to
linear time recognition algorithms. Haskins and Rose introduced the class of chordal
digraphs as a digraph analogue of chordal graphs. Chordal digraphs can be defined
in terms of vertex orderings and several results about chordal graphs can be extended
to chordal digraphs. However, a forbidden subdigraph characterization of chordal
digraphs is not known and finding such a characterization seems to be a difficult
problem. Meister and Telle studied semi-complete chordal digraphs and gave a forbidden
subdigraph characterization of this class of digraphs.
In this thesis, we study chordal digraphs within the classes of quasi-transitive,
extended semi-complete, and locally semi-complete digraphs. For each of these classes
we obtain a forbidden subdigraph characterization of digraphs which are chordal.
We also introduce in this thesis a new variant of chordal digraphs called semi-strict
chordal digraphs. We obtain a forbidden subdigraph characterization of semi-strict
chordal digraphs for each of the classes of semi-complete, quasi-transitive, extended
semi-complete, and locally semi-complete digraphs. === Graduate |
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