Doubly eulerian trails on rectangular grids

✍ Scribed by J. L. Brenner; R. C. Lyndon

• Publisher: John Wiley and Sons
• Year: 1984
• Tongue: English
• Weight: 317 KB
• Volume: 8
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/jgt.3190080306

✦ Synopsis

Let K be the 1-skeleton of the regular tessellation of Euclidean n-space by n-cubes, n 2 2. We show that K admits a doubly Eulerian trail (simply Eulerian trai/),that is,.a doubly infinite path 7~ = 1.. e-,e,e, where, out of each pair {e, e -' } of oppositely directed edges, both (exactly one) appeads) exactly once in 7 ~. and where no e, , , = e;' (there are no Uturns).