2023/04/13 by Grahame Erskine, Terry S. Griggs, Erskine, Grahame +5
Computer Science · Mathematics · #05C45 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2304.11021
openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.