Darryn Bryant

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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)
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)