MATH 7233 — Graph Theory
4 semester hoursGraduateLectureusually offered: falltypical days: M/WBostonTraditional
Covers fundamental concepts in graph theory. Topics include adjacency and incidence matrices, paths and connectedness, and vertex degrees and counting; trees and distance including properties of trees, distance in graphs, spanning trees, minimum spanning trees, and shortest paths; matchings and factors including matchings in bipartite graphs, Hall’s matching condition, and min-max theorems; connectivity, such as vertex connectivity, edge connectivity, k-connected graphs, and Menger’s theorem; network flows including maximum network flow, and integral flows; vertex colorings, such as upper bounds, Brooks, theorem, graphs with large chromatic number, and critical graphs; Eulerian circuits and Hamiltonian cycles including Euler’s theorem, necessary conditions for Hamiltonian cycles, and sufficient conditions; planar graphs including embeddings and Euler’s formula, characterization of planar graphs (Kuratowski’s theorem); and Ramsey theory including Ramsey’s theorem, Ramsey numbers, and graph Ramsey theory.
Offering history
| Term | Sections | Enrolled | Capacity | Full | Open seats/section |
|---|---|---|---|---|---|
| Fall 2023 | 1 | 23 | 35 | 66% | 12.0 |
| Fall 2024 | 1 | 14 | 30 | 47% | 16.0 |
| Fall 2025 | 1 | 9 | 35 | 26% | 26.0 |
Snapshots from scheduled scrapes — not live seat availability. "Full" can exceed 100% when sections over-enroll.
Meeting times
Share of recent sections by weekday: M 100% · T 0% · W 100% · Th 0% · F 0%
Common patterns: MW (100% of sections) — in patterns, R means Thursday
Professors
Fall
- Gabor Lippner (100% of students) · reviews
Percentages are each professor's average share of the season's enrolled students in recent terms.
Links
Official catalog (MATH course descriptions) · Student reviews on RateMyHusky · All MATH courses · Plan it at numap.app