Topic summary · Student revision
Route Inspection Topic Review summary
Self-review on the Chinese Postman problem: odd vertices, pairings, and shortest closed tours.
Files: Topic-Review-Route-Inspection.pdf · Topic-Review-Route-Inspection-Answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Eulerian if all degrees even — a closed trail covers every edge.
- Semi-Eulerian if exactly two odd vertices — open trail starts/ends there.
- For a closed tour with odd vertices, add duplicate edges from a minimum pairing.
- Consider all pairings of odd vertices; choose the least total added length.
- Final length = network total + length of duplicated paths.
Worked example 1 — Odds
Network has 4 odd vertices. What must you do for a closed tour?
Working
Try all pairing options.
Worked example 2 — Euler
All degrees even. Chinese postman length?
Working
No duplication needed.
Worked example 3 — Practice point 1
Apply this idea from the Topic Review: Eulerian if all degrees even — a closed trail covers every edge.
Working
Attempt without notes, then check the answers PDF.
Worked example 4 — Practice point 2
Apply this idea from the Topic Review: Semi-Eulerian if exactly two odd vertices — open trail starts/ends there.
Working
Attempt without notes, then check the answers PDF.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.