A new approach to constructing exponentially many nonisomorphic nonorientable triangular embeddings of complete graphs

0Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.

Abstract

We prove a theorem that for an integer s ≥ 0, if 12 s + 7 is a prime number, then the number of nonisomorphic face 3-colorable nonorientable triangular embeddings of Kn, where n = (12 s + 7) (6 s + 7), is at least 2n3 / 2 (sqrt(2) / 72 + o (1)). By some number-theoretic arguments there are an infinite number of integers s satisfying the hypothesis of the theorem. The theorem is the first known example of constructing at least 2α nℓ + o (nℓ), ℓ > 1, nonisomorphic nonorientable triangular embeddings of Kn for n = 6 t + 1, t ≡ 2 mod 3. To prove the theorem, we use a new approach to constructing nonisomorphic triangular embeddings of complete graphs. The approach combines a cut-and-paste technique and the index one current graph technique. A new connection between Steiner triple systems and constructing triangular embeddings of complete graphs is given. © 2007 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Korzhik, V. P., & Kwak, J. H. (2008). A new approach to constructing exponentially many nonisomorphic nonorientable triangular embeddings of complete graphs. Discrete Mathematics, 308(7), 1072–1079. https://doi.org/10.1016/j.disc.2007.03.060

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free