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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


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