Perfect Graphs and its Extensions

This thesis investigates perfect graphs and its extensions, focusing on induced and non-induced star-perfect graphs, as well as strongly-perfect graphs. It presents an alternative proof to Lovász's characterization (1972) and characterizes induced star-perfect graphs in terms of minimal forbidd...

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Bibliographic Details
Main Author: Alex, James
Format: Thesis
Published: Curtin University 2025
Online Access:http://hdl.handle.net/20.500.11937/98074
Description
Summary:This thesis investigates perfect graphs and its extensions, focusing on induced and non-induced star-perfect graphs, as well as strongly-perfect graphs. It presents an alternative proof to Lovász's characterization (1972) and characterizes induced star-perfect graphs in terms of minimal forbidden induced subgraphs. The thesis also identifies classes of non-induced star-perfect graphs and formulates its invariants using integer-programming. Additionally, a new list of sp-critical graphs and a sufficient condition for a graph to be strongly-perfect is presented.