Basic embeddings into a product of graphs

✍ Scribed by V. Kurlin

• Book ID: 104295555
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 255 KB
• Volume: 102
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00147-3

✦ Synopsis

The notion of a basic embedding appeared in research motivated by Kolmogorov-Arnold's solution of Hilbert's 13th problem. Let K, X, Y be topological spaces.

Theorem. There exists only a finite number of 'prohibited' subgraphs for basic embeddings into R × T n . Consequently, for a finite graph K there is an algorithm for checking whether K is basically embeddable into R × T n . Our theorem is a generalization of Skopenkov's description of graphs basically embeddable into R 2 , and our proofs is a (non-trivial) extension of that one.