Topic summary · Decision maths (D1)
Route Inspection summary
Route inspection (Chinese Postman) finds a shortest closed walk covering every edge by pairing odd-degree vertices optimally.
Files: D1-Route Inspection.pdf · D1-Route Inspection answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- An Eulerian circuit exists when every vertex has even degree.
- With odd vertices, duplicate a shortest pairing of those vertices.
- Four odd vertices give three pairing cases — check each.
- Final length = network total + added pairing length.
Worked example 1 — Two odd vertices
Connected graph with exactly two odd vertices. What do you add?
Working
That pairing makes all degrees even.
Worked example 2 — An Eulerian circuit exists when every vertex has even
Use this method from the Route Inspection sheet: An Eulerian circuit exists when every vertex has even degree.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 3 — With odd vertices, duplicate a shortest pairing of thos
Use this method from the Route Inspection sheet: With odd vertices, duplicate a shortest pairing of those vertices.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 4 — Four odd vertices give three pairing cases — check each
Use this method from the Route Inspection sheet: Four odd vertices give three pairing cases — check each.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 5 — Final length = network total + added pairing length
Use this method from the Route Inspection sheet: Final length = network total + added pairing length.
Working
Each key learning point matches a question type on the printable worksheet.
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.