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|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
|Appears in Collections:||MATH Doctoral Theses|
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