Math 2.0

Combinatorics Definition

Hamiltonian cycle

Builds on Cycle

Definition

Let GG be a graph. A Hamiltonian cycle of GG is a cycle in GG that contains every vertex of GG.

Remarks

A Hamiltonian path is a path that contains every vertex of GG. The names come from William Rowan Hamilton. His icosian game asks for a Hamiltonian cycle on the edges of a dodecahedron. To decide whether a graph has a Hamiltonian cycle is an NP-complete problem.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionTrail, definition, no evidence levelTraildefinitionCircuit, definition, no evidence levelCircuitdefinitionCycle, definition, no evidence levelCycledefinitionHamiltonian cycle, definition, no evidence levelHamiltonian cycledefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Trail definition
  4. Circuit definition
  5. Cycle definition
  6. Hamiltonian cycle definition

Where this leads

3 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Hamiltonian_path, Definitions
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