Three lecture decks, as problems you have to solve.
Nine modules, every one auto-graded, every one generating a fresh problem each time — so you cannot memorise an answer key. Weighted toward the drawing-and-justifying questions that carry the marks on your exercise sheets.
- 01
Definition Traps
Rapid-fire questions built on the exact confusions that lose marks: walk vs trail vs path, circuit vs cycle, subgraph vs induced vs spanning, adjacent vs incident.
not started
- 02
Graph Inspector
Read a graph cold and report n, m, δ, Δ, degree sequence, k(G), distance, diameter and bipartiteness. Every field must be right.
not started
- 03
Edge-Set Builder
Build E(G) by hand for number-set graphs (i+j ∈ S or |i−j| ∈ S) and word graphs. New set every time.
Q1, Q2 · 4–6 marks · not started
- 04
Walks, Trails & Paths
Click a vertex sequence to satisfy a spec — including specs where the honest answer is “does not exist”.
Q4, Ex 5 · 4 marks · not started
- 05
Subgraph Surgery
Produce G − X, G − U and the induced subgraph G[S]. The induced case is where marks quietly disappear.
Ex 4 · 4 marks · not started
- 06
Classes & Operations
Kₙ, Cₙ, Pₙ, K_{s,t}, complements, bipartiteness, distance and diameter — plus G ∪ H, the join G + H and the Cartesian product G × H.
Ex 1–3 · 9 marks · not started
- 07
Degree & Handshake
The First Theorem of Graph Theory under time pressure: counting problems, parity arguments, pseudograph loops, indegree and outdegree.
Ex 3 · 4 marks · not started
- 08
Construction Challenges
Draw a graph meeting a spec — or prove it cannot exist. This is Exercise 1, the biggest single block of marks on the sheet.
Ex 1 · 21 marks · not started
- EX
Exam Simulator
A timed mixed paper drawn from every module, marked the way your exercise sheets are marked, with a per-topic breakdown at the end telling you exactly what to revise next.
no attempts