We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus g 2. This describes the set of unit tangent vectors for which the associated o...
Curves of parameter values for which an asymptotic value of F,(z) = 1 + e-z lies on a pre-pole of arbitrary order are found through an iterative method. Some of these curves are sh...
Let m1, m2, . . . , mt be a list of integers. It is shown that there exists an integer N such that for all n ≥ N, the complete graph of order n can be decomposed into edge-disjo...
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...