Curriculum · Olympiad Topics · Graph Theory
Graph Theory, First Steps
Vertices, edges, degrees, connectivity — and the handshake lemma's surprising reach.
Objectives
- Model problems as graphs
- Apply the handshake lemma
- Argue about connectivity and cycles
The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Graph Theory mastery now.
Train the topic
●●●●○At a party of people, is it possible that everyone shakes hands with exactly others? Enter the number of such handshake configurations if impossible, enter .Olympiad classic●●●○○How many edges does the complete graph have?AMC 10 style●●●●○A tree has vertices. How many edges does it have?Olympiad training