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West, Douglas B. Barrus, Michael David 2015-09-28T15:20:11Z 2015-09-28T15:20:11Z 10000-01-01 2009 2009 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. Made available in DSpace on 2015-09-28T15:20:11Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3362726.pdf: 1996244 bytes, checksum: bdd98e84d113852202e15dcf7288664d (MD5) Previous issue date: 2009 Embargo set by: Seth Robbins for item 88202 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 134 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. http://hdl.handle.net/2142/86921 (MiAaPQ)AAI3362726 eng Mathematics On Induced Subgraphs, Degree Sequences, and Graph Structure text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.