6533b7cefe1ef96bd1257050

RESEARCH PRODUCT

Three-page encoding and complexity theory for spatial graphs

Vitaliy Kurlin

subject

Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Algebra and Number TheoryDegree (graph theory)Semigroup010102 general mathematicsGeometric topologyGeometric Topology (math.GT)01 natural sciences57M25 57M15 57M05Combinatorics010104 statistics & probabilityMathematics - Geometric TopologyCone (topology)Additive functionEncoding (memory)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: Mathematics0101 mathematicsUnit (ring theory)Ambient isotopyMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsofComputing_DISCRETEMATHEMATICS

description

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.

yearjournalcountryeditionlanguage
2004-07-19
https://hal.archives-ouvertes.fr/hal-00013009