Math 2.0

Combinatorics Definition

Hamiltonian graph

Builds on Hamiltonian cycle

Definition

A graph is Hamiltonian if it has a Hamiltonian cycle.

Remarks

The cycle graph CnC_n and the complete graph KnK_n for n≥3n \ge 3 are Hamiltonian. A tree is not Hamiltonian, because it has no cycle. The Petersen graph is not Hamiltonian. Dirac's theorem and Ore's theorem give sufficient conditions in terms of degrees.

Reading path

To understand this page from the ground up, read these 7 pages in order. The foundations come first.

Show the path as a graph
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 cycledefinitionHamiltonian graph, definition, no evidence levelHamiltonian graphdefinition
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
  7. Hamiltonian graph definition

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Hamiltonian_path, Definitions
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MSC05C45
DefinesHamiltonian graph
UsesHamiltonian cycle

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