HUNTERTUTORING

Study Guide — Graph algorithms and structures

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Graph theory & combinatorics

Undergraduate study guide for Graph algorithms and structures.

What this standard means

  • Breadth-first and depth-first search
  • Shortest paths: Dijkstra's algorithm (introduction)
  • Matchings and Hall's marriage theorem (statement)
  • Vertex and edge colorings; chromatic number
  • Ramsey theory (introduction)

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Use trees or tables for counting 2. State the proof method up front 3. Check small cases before generalizing

_See printable PDF for diagram._

Common mistakes

  • Double counting
  • Missing base case in induction

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Graph algorithms and structures.

  • [ ] Applies counting principles correctly
  • [ ] Writes structured proofs
  • [ ] Models problems with graphs or recurrences

Materials for this standard

  • Practice Problems — 20 printable sets
  • Review — 10 difficulty levels
  • Practice Test — 10 difficulty levels
  • Answer key — for parents and tutors

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

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