ARRANGEMENT OF A GRAPH IN A PLANE (RASPOLOZHENIE GRAFA NA PLOSKOSTI),
Abstract
The following two problems arise in the automatic designing of computers: (1) Find an effective algorithm applicable to any graph G and determining whether or not the graph is planar; (2) Find an effective algorithm applicable to any planar graph G and determining the cyclic orders induced by a certain planar realization of the graph G. It is proven that, in solving the above problems, it is sufficient to find the graphs which possess these properties: (a) the graph has no coupling point; (b) the degree of each node is not less than 3. Two lemmas are proven: (1) if the graph G is planar, then for any of its cycles micro, the graph R micro will be bichromatic; (2) if the graph R micro, a planar realization exists which induces this hue. On the above basis, a method of constructing a system of cycles with their bichromatic hues is described.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 02, 1967
- Accession Number
- AD0678431
Entities
People
- G. S. Plesnevich
Organizations
- National Air and Space Intelligence Center