|
HKUST Institutional Repository >
Mathematics >
MATH Doctoral Theses >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1783.1/7530
|
| Title: | Arc ideals and Cohen-Macaulay digraphs |
| Authors: | Wang, Wenjie |
| Issue Date: | 2009 |
| Abstract: | In this thesis I introduce the concepts of arc ideals, unmixed digraphs, and Cohen-Macaulay digraphs, and study their algebraic and combinatorial properties by using commutative algebra and graph theory. The main results are the complete characterizations of the unmixed digraphs with δ > 0 and Cohen-Macaulay digraphs.
The thesis consists of five chapters, which are organized as follows.
Chapter 1 provides the algebraic backgrounds which are needed in the thesis with the aim of introducing the Cohen-Macaulay rings and Cohen-Macaulay modules.
Chapter 2 presents the basic terminology and notion for graphs and digraphs, a short exposition of matching theory, and some relevant results on two types of digraphs: acyclic digraphs and transitive digraphs.
Chapter 3 mainly includes the theory of Stanley-Reisner rings, combinatorial topological characterization of Cohen-Macaulay complexes, and the properties of the Hibi ideals.
Chapter 4 and Chapter 5 are dedicated to the applications of the previous chapters to the study of digraphs, in which unmixed digraphs and Cohen-Macaulay digraphs are characterized. |
| Description: | Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2009
ix, 69 p. : ill. ; 30 cm
HKUST Call Number: Thesis MATH 2009 Wang |
| URI: | http://hdl.handle.net/1783.1/7530 |
| Appears in Collections: | MATH Doctoral Theses
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| th_redirect.html | | 0Kb | HTML | View/Open |
|
All items in this Repository are protected by copyright, with all rights reserved.
|
