SLO

Search the repository

A- | A+ | Print

Query:	search in
	search in
	search in
	search in
Work type:	* old and bologna study programme
Language:
Search in:
Options:	Show only hits with full text
	Reset

1 - 2 / 2

Mutually avoiding Eulerian circuits
Grahame Erskine, Terry S. Griggs, Robert Lewis, James Tuite, 2026, original scientific 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.
Keywords: Eulerian circuit, avoidance
Published in RUP: 20.08.2026; Views: 200; Downloads: 5
Full text (359,50 KB)

On bipartite (1,1,k)-mixed graphs
Cristina Dalfó, Grahame Erskine, Geoffrey Exoo, Miquel Àngel Fiol, James Tuite, 2025, original scientific article

Abstract: Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs, in terms of the number of vertices, are presented for small diameters. Moreover, two infinite families of such graphs with diameter k and number of vertices of the order of 2k/2 are proposed, one of them being totally regular (1,1)-mixed graphs. In addition, we present two more infinite families called chordal ring and chordal double ring mixed graphs, which are bipartite and related to tessellations of the plane. Finally, we give an upper bound that improves the Moore bound for bipartite mixed graphs for r = z = 1.
Keywords: mixed graph, degree/diameter problem, Moore bound, bipartite graph
Published in RUP: 03.11.2025; Views: 1440; Downloads: 8
Full text (628,98 KB)

Search done in 0 sec.