Search Results - "Burgess, Andrea C"

Existential Closure in Line Graphs by Burgess, Andrea C., Luther, Robert D., Pike, David A.

“…A graph is n - existentially closed if, for all disjoint sets of vertices A and B with | A ∪ B | = n , there is a vertex z not in A ∪ B adjacent to each vertex…”
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The edge‐connectivity of vertex‐transitive hypergraphs by Burgess, Andrea C., Luther, Robert D., Pike, David A.

“…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…”
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The firebreak problem by Barnetson, Kathleen D., Burgess, Andrea C., Enright, Jessica, Howell, Jared, Pike, David A., Ryan, Brady

“…Suppose we have a network that is represented by a graph G. Potentially a fire (or other type of contagion) might erupt at some vertex of G. We are able to…”
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Colouring even cycle systems by Burgess, Andrea C., Pike, David A.

“…An m-cycle system of order n is a partition of the edges of the complete graph K n into m-cycles. An m-cycle system S is said to be weakly k-colourable if its…”
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Generalized packing designs by Bailey, Robert F., Burgess, Andrea C.

“…Generalized t-designs, which form a common generalization of objects such as t-designs, resolvable designs and orthogonal arrays, were defined by Cameron [P.J…”
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On generalized Howell designs with block size three by Abel, R. Julian R., Bailey, Robert F., Burgess, Andrea C., Danziger, Peter, Mendelsohn, Eric

“…In this paper, we examine a class of doubly resolvable combinatorial objects. Let t , k , λ , s and v be nonnegative integers, and let X be a set of v symbols…”
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Packing Designs with large block size by Burgess, Andrea C, Danziger, Peter, Javed, Muhammad Tariq

“…Given positive integers $v,k,t$ and $\lambda$ with $v \geq k \geq t$, a {packing design} PD$_{\lambda}(t,k,v)$ is a pair $(V,\mathcal{B})$, where $V$ is a…”
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Existential Closure in Uniform Hypergraphs by Burgess, Andrea C, Luther, Robert D, Pike, David A

“…For a positive integer $n$, a graph with at least $n$ vertices is $n$-existentially closed or simply $n$-e.c. if for any set of vertices $S$ of size $n$ and…”
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Extending Graph Burning to Hypergraphs by Burgess, Andrea C, Jones, Caleb W, Pike, David A

“…Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph…”
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Proportion-Based Hypergraph Burning by Burgess, Andrea C, Hawkin, John A, Howse, Alexander J. M, Jones, Caleb W, Pike, David A

“…Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This…”
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Existential Closure in Line Graphs by Burgess, Andrea C, Luther, Robert D, Pike, David A

“…A graph $G$ is {\it $n$-existentially closed} if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$…”
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Generalized covering designs and clique coverings by Bailey, Robert F., Burgess, Andrea C., Cavers, Michael S., Meagher, Karen

“…Inspired by the “generalized t‐designs” defined by Cameron [P. J. Cameron, Discrete Math 309 (2009), 4835–4842], we define a new class of combinatorial designs…”
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Weak colourings of Kirkman triple systems by Burgess, Andrea C, Cavenagh, Nicholas J, Danziger, Peter, Pike, David A

“…A $\delta$-colouring of the point set of a block design is said to be {\em weak} if no block is monochromatic. The {\em weak chromatic number} $\chi(S)$ of a…”
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The Edge-Connectivity of Vertex-Transitive Hypergraphs by Burgess, Andrea C, Luther, Robert D, Pike, David A

“…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…”
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Mutually orthogonal cycle systems by Burgess, Andrea C, Cavenagh, Nicholas J, Pike, David A

“…An ${\ell}$-cycle system ${\mathcal F}$ of a graph $\Gamma$ is a set of ${\ell}$-cycles which partition the edge set of $\Gamma$. Two such cycle systems…”
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Distance-Restricted Firefighting on Finite Graphs by Burgess, Andrea C, Hawkin, John, Howse, Alexander, Marcoux, John, Pike, David A

“…In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph $G$ and then $b$ firefighters protect $b$…”
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Cops that surround a robber by Burgess, Andrea C, Cameron, Rosalind A, Clarke, Nancy E, Danziger, Peter, Finbow, Stephen, Jones, Caleb W, Pike, David A

“…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…”
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The Firebreak Problem by Barnetson, Kathleen D, Burgess, Andrea C, Enright, Jessica, Howell, Jared, Pike, David A, Ryan, Brady

“…Suppose we have a network that is represented by a graph $G$. Potentially a fire (or other type of contagion) might erupt at some vertex of $G$. We are able to…”
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Coloring 4-cycle systems by Burgess, Andrea C., Pike, David A.

“…An m‐cycle system of order n is a partition of the edges of the complete graph Kn into m‐cycles. We investigate k‐colorings of 4‐cycle systems in which no…”
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Generalized packing designs by Bailey, Robert F, Burgess, Andrea C

“…Generalized $t$-designs, which form a common generalization of objects such as $t$-designs, resolvable designs and orthogonal arrays, were defined by Cameron…”
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