Graph theory — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Graph theory — a combinatorics concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
Filter by difficulty
These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
2006 AMC 10A Problem 25 • 2010 AMC 10A Problem 20 • 2011 AMC 10A Problem 22 • 2012 AMC 10A Problem 23 • 2012 AMC 10B Problem 15 • 2015 AMC 10B Problem 20 • 2016 AMC 10B Problem 22 • 2020 AMC 10A Problem 19 • 2020 AMC 10B Problem 17 • 2021 AMC 10B Fall Problem 23 • 2023 AMC 10A Problem 18 • 2023 AMC 10A Problem 25 • 2025 AMC 10B Problem 16
AMC 12
1957 AMC 12 Problem 17 • 1967 AMC 12 Problem 38 • 1978 AMC 12 Problem 16 • 2006 AMC 12A Problem 20 • 2011 AMC 12A Problem 16 • 2012 AMC 12A Problem 19 • 2013 AMC 12B Problem 12 • 2016 AMC 12B Problem 20 • 2017 AMC 12A Problem 5 • 2019 AMC 12A Problem 13 • 2019 AMC 12B Problem 10 • 2020 AMC 12B Problem 15 • 2021 AMC 12A Fall Problem 16 • 2022 AMC 12A Problem 7 • 2023 AMC 12A Problem 21 • 2024 AMC 12A Problem 22 • 2025 AMC 12B Problem 13
AIME
1985 AIME Problem 14 • 1989 AIME Problem 13 • 1996 AIME Problem 6 • 1998 AIME Problem 15 • 2001 AIME I Problem 15 • 2012 AIME II Problem 14 • 2016 AIME I Problem 3 • 2016 AIME II Problem 12 • 2017 AIME II Problem 11 • 2022 AIME II Problem 9 • 2023 AIME I Problem 14 • 2023 AIME II Problem 11 • 2025 AIME II Problem 11 • 2026 AIME II Problem 15