33 citations · 44 across the 7 of their papers we have counts for
7 papers
Whitney's Theorem for 2-Regular Planar Digraphs
Dan Archdeacon, Matt DeVos, Stefan Hannie +1
A digraph is 2-regular if every vertex has both indegree and outdegree two. We define an embedding of a 2-regular digraph to be a 2-cell embedding of the underlying graph in a clos…
Embedding Quartic Eulerian Digraphs on the Plane
Dan Archdeacon, Paul Bonnington, Bojan Mohar
Minimal obstructions for embedding 4-regular Eulerian digraphs on the plane are considered in relation to the partial order defined by the cycle removal operation. Their basic prop…
-restricted Double Traces
Dan Archdeacon, Luis Goddyn, Jernej Rus
For a graph and , an -restricted strong trace is a closed walk which traverses every edge from once in each direction and every other edge twice in the…
Tight Heffter Arrays Exist for all Possible Values: The Research Report
Dan S. Archdeacon, Tomas Boothby, Jeffrey H. Dinitz
A tight Heffter array H(m,n) is an m x n matrix with nonzero entries from Z_{2mn+1} such that i) the sum of the elements in each row and each column is 0, and ii) no element from {…
On Partial Sums in Cyclic Groups
D. S. Archdeacon, J. H. Dinitz, A. Mattern +1
We are interested in ordering the elements of a subset A of the non-zero integers modulo n in such a way that all the partial sums are distinct. We conjecture that this can always…
Square Integer Heffter Arrays with Empty Cells
D. S. Archdeacon, J. H. Dinitz, D. M. Donovan +1
A Heffter array is an matrix with nonzero entries from such that each row contains filled cells and each column contains …
Heffter Arrays and Biembedding Graphs on Surfaces
Dan Archdeacon
A Heffter array is an m by n matrix with nonzero entries from Z_{2mn+1} such that i) every row and column sum to 0, and ii) no element from {x,-x} appears twice. We construct some…