On Halin graphs
The paper deals with a subfamily of those planar graphs which have outerplanar intersection of their MacLane cycle basis. These graphs have been known as Halin graphs. Their connectivity properties, structure of cycles, and feasible embeddings in the plane are discussed here. This paper also presents some initial investigations of NP-complete problems restricted to the family of Halin graphs.
KeywordsPlanar Graph Chromatic Number Hamiltonian Cycle Intersection Graph Interior Vertex
Unable to display preview. Download preview PDF.
- J.A. Bondy, Pancyclic graphs: recent results, in: A. Hajnal. R. Rado and V.T. Sós (eds.), Infinite and Finite Sets, Colloquia Mathematica Societatis János Bolyai, vol. 10, Kiado (Budapest) and North-Holland (Amsterdam), (1975), 181–187.Google Scholar
- R. Halin, Studies in minimally connected graphs, in: Combinatorial Mathematics and its Applications, D.J.A. Weish (ed.), Academic Press, (1971), 129–136.Google Scholar
- L. Lovász and M.D. Plummer, On a family of planar bioritical graphs, Proc. London Math. Soc., 30 (1975), 187–203.Google Scholar
- J. Malkevitch, Cycle lengths in polytopal graphs, in: Y. Alavi and D.R. Lick (eds.), Theory and Applications of Graphs, Springer-Verlag, (1978), 364–370.Google Scholar