On Induced Subgraphs, Degree Sequences, and Graph Structure
Barrus, Michael David
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https://hdl.handle.net/2142/86921
Description
Title
On Induced Subgraphs, Degree Sequences, and Graph Structure
Author(s)
Barrus, Michael David
Issue Date
2009
Doctoral Committee Chair(s)
West, Douglas B.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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