Mathematics
https://qmro.qmul.ac.uk/xmlui/handle/123456789/33697
Sat, 23 Feb 2019 00:24:01 GMT2019-02-23T00:24:01ZTHE SHARP THRESHOLD FOR JIGSAW PERCOLATION IN RANDOM GRAPHS
https://qmro.qmul.ac.uk/xmlui/handle/123456789/55505
THE SHARP THRESHOLD FOR JIGSAW PERCOLATION IN RANDOM GRAPHS
MAKAI, T; Cooley, O; Kapetanopoulos, T
We analyse the jigsaw percolation process, which may be seen as a measure of whether two graphs on the same vertex set are `jointly connected'. Bollobás, Riordan, Slivken and Smith proved that when the two graphs are independent binomial random graphs, whether the jigsaw process percolates undergoes a phase transition when the product of the two probabilities is...
Tue, 01 Jan 2019 00:00:00 GMThttps://qmro.qmul.ac.uk/xmlui/handle/123456789/555052019-01-01T00:00:00ZPower substitution in quasianalytic Carleman classes
https://qmro.qmul.ac.uk/xmlui/handle/123456789/55487
Power substitution in quasianalytic Carleman classes
Buhovski, L; Kiro, A; SODIN, A
Consider an equation of the form f(x)=g(xk), where k>1 and f(x) is a function in a given Carleman class of smooth functions. For each k, we construct a Carleman-type class which contains all the smooth solutions g(x) to such equations. We prove, under regularity assumptions, that if the original Carleman class is quasianalytic, then so is the new class. The results admit an extension to multivariate functions.
Tue, 01 Jan 2019 00:00:00 GMThttps://qmro.qmul.ac.uk/xmlui/handle/123456789/554872019-01-01T00:00:00ZOn a biased edge isoperimetric inequality for the discrete cube
https://qmro.qmul.ac.uk/xmlui/handle/123456789/55485
On a biased edge isoperimetric inequality for the discrete cube
Ellis, D; Keller, N; Lifshitz, N
The ‘full’ edge isoperimetric inequality for the discrete cube (due to Harper, Lindsey, Berstein and Hart) specifies the minimum size of the edge boundary...
Mon, 01 Apr 2019 00:00:00 GMThttps://qmro.qmul.ac.uk/xmlui/handle/123456789/554852019-04-01T00:00:00ZSemi-perfect 1-Factorizations of the Hypercube
https://qmro.qmul.ac.uk/xmlui/handle/123456789/55404
Semi-perfect 1-Factorizations of the Hypercube
BEHAGUE, NC
A 1-factorization M = {M_1,M_2,...,M_n} of a graph G is called perfect if the union of any pair of 1-factors M_i, M_j with i ≠ j is a Hamilton cycle. It is called k-semi-perfect if the union of any pair of 1-factors M_i, M_j with 1 ≤ i ≤ k and k < j ≤ n is a Hamilton cycle. We consider 1-factorizations of the discrete cube Q_d. There is no perfect 1-factorization of Q_d, but it was previously shown that there is a 1-semi-perfect 1-factorization of Q_d for all d. Our main result is to prove that there is a k-semi-perfect 1-factorization of Q_d for all k and all d, except for one possible exception when k=3 and d=6. This is, in some sense, best possible. We conclude with some questions concerning other generalisations of perfect 1-factorizations.
Tue, 01 Jan 2019 00:00:00 GMThttps://qmro.qmul.ac.uk/xmlui/handle/123456789/554042019-01-01T00:00:00Z