13 citations · 35 across the 16 of their papers we have counts for
18 papers
On the spouse-loving variant of the Oberwolfach problem
Noah Bolohan, Iona Buchanan, Andrea Burgess +2
We prove that , the complete graph of an even order with a -factor duplicated, admits a decomposition into -factors, each a disjoint union of cycles of length $m \geq…
A survey on constructive methods for the Oberwolfach problem and its variants
Andrea Burgess, Peter Danziger, Tommaso Traetta
The generalized Oberwolfach problem asks for a decomposition of a graph into specified 2-regular spanning subgraphs , called factors. The classic Oberwolfach p…
Distance-Restricted Firefighting on Finite Graphs
Andrea C. Burgess, John Hawkin, Alexander Howse +2
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph and then firefighters protect vertices. On each subsequent…
Existential Closure in Line Graphs
Andrea C. Burgess, Robert D. Luther, David A. Pike
A graph is {\it -existentially closed} if, for all disjoint sets of vertices and with , there is a vertex not in adjacent to each vertex o…
Constructing uniform 2-factorizations via row-sum matrices: solutions to the Hamilton-Waterloo problem
A. C. Burgess, P. Danziger, A. Pastine +1
In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group . When is cyclic, these types of matrices have been widely used to build uniform…
The Edge-Connectivity of Vertex-Transitive Hypergraphs
Andrea C. Burgess, Robert D. Luther, David A. Pike
A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-…
Firefighting with a Distance-Based Restriction
Andrea Burgess, John Marcoux, David Pike
In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph and then firefighters protect vertices. On each subsequent…
Mutually orthogonal cycle systems
Andrea C. Burgess, Nicholas J. Cavenagh, David A. Pike
An -cycle system of a graph is a set of -cycles which partition the edge set of . Two such cycle systems and ar…
On the Oberwolfach problem for single-flip -factors via graceful labelings
A. C. Burgess, P. Danziger, T. Traetta
Let be a -regular graph of order . The Oberwolfach problem , posed in 1967 and still open, asks for a decomposition of into copies of . In this paper we s…
Cops that surround a robber
Andrea C. Burgess, Rosalind A. Cameron, Nancy E. Clarke +4
We introduce the game of Surrounding Cops and Robbers on a graph, as a variant of the original game of Cops and Robbers. In contrast to the original game in which the cops win by o…
Cyclic cycle systems of the complete multipartite graph
Andrea Burgess, Francesca Merola, Tommaso Traetta
In this paper, we study the existence problem for cyclic -cycle decompositions of the graph , the complete multipartite graph with parts of size , and give nec…
The Firebreak Problem
Kathleen D. Barnetson, Andrea C. Burgess, Jessica Enright +3
Suppose we have a network that is represented by a graph . Potentially a fire (or other type of contagion) might erupt at some vertex of . We are able to respond to this outb…
The Hamilton-Waterloo Problem with even cycle lengths
A. C. Burgess, P. Danziger, T. Traetta
The Hamilton-Waterloo Problem HWP asks for a 2-factorization of the complete graph or , the complete graph with the edges of a 1-factor removed, into …
On the Hamilton-Waterloo Problem with cycle lengths of distinct parities
Andrea Burgess, Peter Danziger, Tommaso Traetta
Let denote the complete graph if is odd and , the complete graph with the edges of a 1-factor removed, if is even. Given non-negative integers $v, M, N…
On the directed Oberwolfach Problem with equal cycle lengths: the odd case
Andrea Burgess, Nevena Francetic, Mateja Sajna
We show that the complete symmetric digraph admits a resolvable decomposition into directed cycles of length for all odd , . Consequently, $K_{…
Zero-sum flows for Steiner triple systems
S. Akbari, A. C. Burgess, P. Danziger +1
Given a - design, , a {\it zero-sum -flow} of is a map such that for any poi…
Generalized packing designs
Robert F. Bailey, Andrea C. Burgess
Generalized -designs, which form a common generalization of objects such as -designs, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A gener…
Generalized covering designs and clique coverings
Robert F. Bailey, Andrea C. Burgess, Michael S. Cavers +1
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinato…