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We prove that all Paley graphs can be decomposed into Hamilton cycles. This paper is dedicated to Gert Sabidussi in celebration of his 80th birthday.

- Darryn Bryant, Padraig´o Catháin
- 2015

For any rational number h and all sufficiently large n we give a deterministic construction for an n × hn compressed sensing matrix with (1 , t)-recoverability where t = O(√ n). Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of-equiangular frames, which we introduce as a generalisation of equiangular tight… (More)

- Mateja Sajna, Andrea Burgess, Peter Danziger, Daniel Horsley, Barbara Maenhaut, Darryn Bryant +1 other
- 2013

Repacking in cycle decompositions. A method which takes a decomposition of a graph into edge-disjoint cycles and produces a decomposition of a new graph into edge-disjoint cycles of the same lengths will be discussed. This method, called repacking, underpins much of the recent progress on cycle decomposition problems. Orthogonally resolvable cycle… (More)

It is shown that if F 1 , F 2 ,. .. , F t are bipartite 2-regular graphs of order n and α 1 , α 2 ,. .. , α t are non-negative integers such that α 1 +α 2 +· · ·+α t = n−2 2 , α 1 ≥ 3 is odd, and α i is even for i = 2, 3,. .. , t, then there exists a 2-factorisation of K n −I in which there are exactly α i 2-factors isomorphic to F i for i = 1, 2,. .. , t.… (More)

We prove that all connected vertex-transitive graphs of order p 2 , p a prime, can be decomposed into Hamilton cycles.

The next article by Darryn and Daniel provides an introduction to the Lindner conjecture and its solution.

The circulant graph of order n with connection set S is denoted by Circ(n, S). Several results on decompositions of Circ(n, {1, 2}) and Circ(n, {1, 2, 3}) are proved here. The existence problems for decom-positions into paths of arbitrary specified lengths and for decomposi-tions into cycles of arbitrary specified lengths are completely solved for Circ(n,… (More)

In graph cleaning problems, brushes clean a graph by traversing it subject to certain rules. Various problems arise, such as determining the minimum number of brushes that are required to clean the entire graph. This number is called the brushing number. Here, we study a new variant of the brushing problem in which one vertex is cleaned at a time, but more… (More)