Accession Number : AD0678431

Title :   ARRANGEMENT OF A GRAPH IN A PLANE (RASPOLOZHENIE GRAFA NA PLOSKOSTI),

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Plesnevich,G. S.

Report Date : 02 NOV 1967

Pagination or Media Count : 11

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.

Descriptors :   (*GRAPHICS, *DATA PROCESSING), TRANSFORMATIONS, COLORS, ALGORITHMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE