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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ndltd-uvic.ca-oai-dspace.library.uvic.ca-1828-110832019-08-30T16:58:48Z On chordal digraphs and semi-strict chordal digraphs Ye, Ying Ying Huang, Jing chordal digraphs semi-strict chordal digraphs semi-complete digraphs locally semi-complete digraphs quasi-transitive digraphs extended-semi-complete 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 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 2019-08-29T18:16:24Z 2019-08-29T18:16:24Z 2019 2019-08-29 Thesis http://hdl.handle.net/1828/11083 English en Available to the World Wide Web application/pdf |
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English en |
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chordal digraphs semi-strict chordal digraphs semi-complete digraphs locally semi-complete digraphs quasi-transitive digraphs extended-semi-complete digraphs |
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chordal digraphs semi-strict chordal digraphs semi-complete digraphs locally semi-complete digraphs quasi-transitive digraphs extended-semi-complete digraphs Ye, Ying Ying On chordal digraphs and semi-strict chordal digraphs |
description |
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 |
author2 |
Huang, Jing |
author_facet |
Huang, Jing Ye, Ying Ying |
author |
Ye, Ying Ying |
author_sort |
Ye, Ying Ying |
title |
On chordal digraphs and semi-strict chordal digraphs |
title_short |
On chordal digraphs and semi-strict chordal digraphs |
title_full |
On chordal digraphs and semi-strict chordal digraphs |
title_fullStr |
On chordal digraphs and semi-strict chordal digraphs |
title_full_unstemmed |
On chordal digraphs and semi-strict chordal digraphs |
title_sort |
on chordal digraphs and semi-strict chordal digraphs |
publishDate |
2019 |
url |
http://hdl.handle.net/1828/11083 |
work_keys_str_mv |
AT yeyingying onchordaldigraphsandsemistrictchordaldigraphs |
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1719239324180938752 |