IB Maths AI HL 3.16 - Tree and Cycle Algorithms Notes

Support graph theory teaching with these IB Maths AI HL 3.16 Tree and Cycle Algorithms notes for Mathematics: Applications and Interpretation Higher Level. Build from precise graph vocabulary to algorithms for connecting networks and finding efficient routes, with structured practice that develops mathematical reasoning.

Topics covered

• Walks, trails, paths, circuits and cycles, including repeated vertices and edges
• Eulerian trails and circuits: vertex degree conditions in connected graphs
• Hamiltonian paths and cycles: visiting every vertex exactly once
• Minimum spanning trees using Kruskal’s and Prim’s algorithms
• Selecting edges, avoiding cycles and finding a minimum total weight
• The Chinese Postman Problem (route inspection), odd vertices and shortest closed routes
• The Travelling Salesman Problem (TSP), including exact searches
• Nearest-neighbour upper bounds and deleted-vertex lower bounds
• Interpreting distance tables, constructing routes and stating a range for the optimal tour

Use for classroom explanation, guided practice, independent study or revision of IB Maths AI HL 3.16 Tree and Cycle Algorithms.

Complete the AHL 3.16 set

• Tree and Cycle Algorithms lesson slides
• Tree and Cycle Algorithms worksheet with answer key