54 citations · 65 across the 10 of their papers we have counts for
14 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…
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 determining when small embeddings of partial Steiner triple systems exist
Darryn Bryant, Ajani De Vas Gunasekara, Daniel Horsley
A partial Steiner triple system of order is a pair where is a set of elements and is a set of triples of elements of such that any t…
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 …
Hamilton path decompositions of complete multipartite graphs
Darryn Bryant, Hao Chuien Hang, Sarada Herke
We prove that a complete multipartite graph with vertices and edges can be decomposed into edge-disjoint Hamilton paths if and only if is an integer an…
Steiner triple systems with high chromatic index
Darryn Bryant, Charles Colbourn, Daniel Horsley +1
It is conjectured that every Steiner triple system of order has chromatic index at most when and at most when $v \equiv 1 \pmod…