2 citations · 3 across the 6 of their papers we have counts for
7 papers
On decomposition thresholds for odd-length cycles and other tripartite graphs
Darryn Bryant, Peter Dukes, Daniel Horsley +2
An (edge) decomposition of a graph is a set of subgraphs of whose edge sets partition the edge set of . Here we show, for each odd , that any graph of s…
An Infinite Family of Connected 1-Factorisations of Complete 3-Uniform Hypergraphs
Barbara Maenhaut, Jeremy Mitchell, Anna Puskas
A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-…
Hamilton decompositions of line graphs
Darryn Bryant, Sara Herke, Barbara Maenhaut +1
It is proved that if a graph is regular of even degree and contains a Hamilton cycle, or regular of odd degree and contains a Hamiltonian -factor, then its line graph is Hamilto…
On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions
Darryn Bryant, Barbara Maenhaut, Benjamin R. Smith
In contrast with Kotzig's result that the line graph of a -regular graph is Hamilton decomposable if and only if is Hamiltonian, we show that for each integer …
On Hamilton Decompositions of Infinite Circulant Graphs
Darryn Bryant, Sarada Herke, Barbara Maenhaut +1
The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected $2k…
Decompositions of complete multigraphs into cycles of varying lengths
Darryn Bryant, Daniel Horsley, Barbara Maenhaut +1
We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint…