# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Hamiltonian embeddings of $K_{n,n,n}$

Presented by Mr. Justin SCHROEDER
Type: Oral presentation
Track: Maps and Symmetries

## Content

A hamiltonian embedding of a graph $G$ is a drawing of $G$ on a surface such that no edges cross and the boundary of every face is a hamilton cycle. In this talk we develop several methods of constructing hamiltonian embeddings of the complete tripartite graph $K_{n,n,n}$. For nonorientable surfaces, we build an embedding for all values of $n$. For orientable surfaces, we build an embedding for all $n\equiv 0,1,3$ (mod 4) and explore some possible constructions when $n\equiv 2$ (mod 4) based on orthogonal latin squares. This is joint work with Mark Ellingham.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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