Cubic graph

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The Petersen graph is a Cubic graph.
The Petersen graph is a Cubic graph.

In the mathematical field of graph theory, a cubic graph is a graph where all vertices are incident to exactly three edges. In other words a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.

A bicubic graph is a cubic bipartite graph.

[edit] History

  • 1934: Ronald M. Foster begins collecting examples of cubic symmetric graphs, forming the start of the Foster census [1].
  • 1971: Tutte conjectured that all bicubic graphs are Hamiltonian. However, Horton provided a 96-vertex counterexample.
  • 2003: Petr Hliněný showed that the problem of finding the crossing number (the minimum number of edges which cross in any graph drawing) of a cubic graph is NP-hard, despite the fact that they have low degree. There are, however, practical approximation algorithms for finding the crossing number of cubic graphs.

[edit] See also

[edit] References


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