Interval graphs admit elegant ordering and structural characterizations. A natural digraph analogue of interval graphs, called chronological interval digraphs, has recently been identified and studied.
We introduce the class of chronological rectangle digraphs, and show that they are a higher dimensional analogue of chronological interval digraphs. A main goal of this thesis is to establish a foundation of knowledge about this class, including basic properties and an ordering characterization. Our most significant result is a forbidden induced subdigraph characterization for the series-parallel digraphs which are chronological rectangle. We also discuss obtaining chronological rectangle digraphs from orientations of graphs.
In addition we introduce the related concept of the chronological interval dimension of a digraph, and determine the digraphs for which it is defined. Unit and proper chronological rectangle digraphs, defined analogously to unit and proper interval graphs, are also introduced and studied. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/6989 |
| Date | 23 December 2015 |
| Creators | Manzer, Joshua Daniel Adrian |
| Contributors | Huang, Jing |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web, http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
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