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Title: The structure of graphs with no cycles of length 0 (mod 3)
Authors: Gauthier, Gregory Joseph
Advisors: Seymour, Paul D
Contributors: Mathematics Department
Keywords: graph
structural graph theory
Subjects: Mathematics
Issue Date: 2017
Publisher: Princeton, NJ : Princeton University
Abstract: We examine the structure of graphs that have no cycles of length 0 (mod 3). We show that, if G is a simple 2-connected graph with no cycles of length 0 (mod 3), then G has two adjacent degree two vertices or G has two nonadjacent degree two vertices with the same neighborhood. Using this result, it follows that if G is a simple graph with no cycles of length 0 (mod 3), then for every induced subgraph H of G, the modularity of H, defined as the number of even independent sets minus the number of odd independent sets, is either −1, 0, or 1.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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