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Description
Title: | On Induced Subgraphs, Degree Sequences, and Graph Structure |
Author(s): | Barrus, Michael David |
Doctoral Committee Chair(s): | West, Douglas B. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Mathematics |
Abstract: | Finally, we define the A4-structure H of a graph G to be the 4-uniform hypergraph on the vertex set of G where four vertices comprise an edge in H if and only if they form the vertex set of an alternating 4-cycle in G. Our definition is a variation of the notion of the P4-structure, a hypergraph which has been shown to have important ties to the various decompositions of a graph. We show that A4-structure has many properties analogous to those of P4-structure, including connections to a special type of graph decomposition called the canonical decomposition. We also give several equivalent characterizations of the class of A4-split graphs, those having the same A4-structure as some split graph. |
Issue Date: | 2009 |
Type: | Text |
Language: | English |
Description: | 134 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. |
URI: | http://hdl.handle.net/2142/86921 |
Other Identifier(s): | (MiAaPQ)AAI3362726 |
Date Available in IDEALS: | 2015-09-28 |
Date Deposited: | 2009 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois