Mutually avoiding Eulerian circuits
Combinatorics
2023-04-24 v1
Abstract
Two Eulerian circuits, both starting and ending at the same vertex, are avoiding if at every other point of the circuits they are at least distance 2 apart. An Eulerian graph which admits two such avoiding circuits starting from any vertex is said to be doubly Eulerian. The motivation for this definition is that the extremal Eulerian graphs, i.e. the complete graphs on an odd number of vertices and the cycles, are not doubly Eulerian. We prove results about doubly Eulerian graphs and identify those that are the `densest' and `sparsest' in terms of the number of edges.
Keywords
Cite
@article{arxiv.2304.11021,
title = {Mutually avoiding Eulerian circuits},
author = {Grahame Erskine and Terry Griggs and Robert Lewis and James Tuite},
journal= {arXiv preprint arXiv:2304.11021},
year = {2023}
}
Comments
22 pages; 9 figures