Work

Mutually avoiding Eulerian circuits

Year: 2025

Type: article

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.

Source: Ars Mathematica Contemporanea

DOI: 10.26493/1855-3974.3220.12a

Authors: Grahame Erskine, Terry S. Griggs, Robert Lewis, James Tuite

Institutions: The Open University, Klaipėda University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: London Mathematical Society, Engineering and Physical Sciences Research Council

Awards: Maths Research Associates 2021 Open, G3399481711