Uniform graph embedding into metric spaces

Компьютерные исследования и моделирование

关键词: metric space;    infinite graph;    factor graph;    Minkowski metric;    Lorenz metric;    Euclid metric;   

DOI  :  10.20537/2076-7633-2012-4-2-241-251

来源: DOAJ

【 摘 要 】

The task of embedding an infinity countable graph into continuous metric space is considered. The concept of uniform embedding having no accumulation point in a set of vertex images and having all graph edge images of a limited length is introduced. Necessary and sufficient conditions for possibility of uniform embedding into spaces with Euclid and Lorenz metrics are stated in terms of graph structure. It is proved that tree graphs with finite branching have uniform embedding into space with absolute Minkowski metric.

【 授权许可】

Unknown