Evalutation: 50% assignments + 50% project
More details to be added later.
Lecture-1: Perfect Matchings, Tutte's Theorem and Matching Covered Graphs (MCGs)
Lecture-2: The Canonical Partition Theorem (due to Kotzig and Lovász)
Lecture-3: Families, Operations and Hetyei's Ear Decompositions for Bipartite MCGs
Lecture-4 Part-I: Separating cuts, tight cuts and barrier cuts
Lecture-4 Part-II: Barrier cuts, 2-separation cuts and the ELP Theorem
Lecture-5: Separating cuts in bipartite graphs, and tight 3-cuts, are barrier cuts
Lecture-6 Part-I: Bricks & Braces, ELP Theorem statement(s), and important families (of bricks & braces)
Lecture-6 Part-II: Tight Cut Decomposition (TCD) procedure and Lovász's Unique Decomposition Theorem
Lecture-7 Part-I: Lovász's (1987) Unique Tight Cut Decomposition Theorem & its proof
Lecture-7 Part-II: Lovász's Unique Tight Cut Decomposition Theorem (proof continued)
Lecture-8: CLM (2002) Theorem (Lovász's Conjecture) & Subadditivity of the b function/invariant (number of bricks)