Week 11: Graph Constraints and Counting
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# Week 11: Graph Constraints and Counting > **Course:** Jan 2026 - Mathematics I > **Focus:** Combining graph limits with counting and structural reasoning. --- ## 1.
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Week 11: Graph Constraints and Counting
Course: Jan 2026 - Mathematics I Focus: Combining graph limits with counting and structural reasoning.
1. Core idea
Week 11 is a constraints week. You do not compute blindly, you prune the search space with graph structure.
What to remember
- Degree lower bounds force edge lower bounds.
- Shortest-path limits strongly constrain BFS depth.
- Matrix powers expose connection information across paths.
- Topological / prerequisite style questions are usually about partial order logic.
2. Common traps
- Forgetting that degree counts touch every incident edge.
- Assuming a graph is possible just because the degree list looks neat.
- Ignoring path-length constraints when reasoning about graph size.
3. Speedrun pattern
When you see a Week 11 question, ask:
- What is the hard constraint?
- What does it imply globally?
- Can I count edges or layers instead of drawing every case?