1 research outputs found
Halin graphs are 3-vertex-colorable except even wheels
A Halin graph is a graph obtained by embedding a tree having no nodes of
degree two in the plane, and then adding a cycle to join the leaves of the tree
in such a way that the resulting graph is planar. According to the four color
theorem, Halin graphs are 4-vertex-colorable. On the other hand, they are not
2-vertex-colorable because they have triangles. We show that all Halin graphs
are 3-vertex-colorable except even wheels. We also show how to find the perfect
elimination ordering of a chordal completion for a given Halin graph. The
algorithms are implemented in Python using the graphtheory package. Generators
of random Halin graphs (general or cubic) are included. The source code is
available from the public GitHub repository.Comment: 8 pages, 2 figure