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Edge-Colouring Hypergraphs Properly (Covering with Matchings) or Polychromatically (Packing Covers)
Edge-Colouring Hypergraphs Properly Polychromatically
2010/12/15
Let the chromatic index of a hypergraph be the smallest number of colours needed to colour the
edges such that similarly-coloured edges are disjoint. Likewise, let the cover index be the maximum numb...
On Cycles in Random Graphs
Cycles Random Graphs
2010/12/15
We consider the geometric random (GR) graph on the d−dimensional torus
with the L distance measure (1 1). Our main result is an exact characterization
of the probability that a particul...
The covering number of a hypergraph H is the largest integer k such that the edges of H can be partitioned into k classes such that every vertex is incident with edges from every class. We
prove a nu...
We de ne the limiting density of a minor-closed family of simple graphs F to be the smallest
number k such that every n-vertex graph in F has at most kn(1+o(1)) edges, and we investigate
the set of ...
The purpose of this note is make Theorem 13 in [2] more accessible.Restatements of the theorem already appeared in few of the authors'succeeding works but with no details. We wish in this note to give...
Let kr(n, δ) be the minimum number of r-cliques in graphs with n vertices and minimum degree δ. We evaluate kr(n, δ) for δ ≤ 4n/5 and some other cases. Moreover, we give a construction, which we conje...
Long cycles in subgraphs of (pseudo)random directed graphs
Long cycles subgraphs of (pseudo)random directed graphs
2010/12/8
We study the resilience of random and pseudorandom directed graphs with respect to the property of having long directed cycles. For every 0 < < 1/2 we find a constant c = c(
) such that the followin...
A conjecture of Carsten Thomassen states that every 4-connected line graph is hamiltonian. It is known that the conjecture is true for 7-connected line graphs. We improve this by showing that any 5-co...
We study the dynamics of Thurston maps under iteration.These are branched covering maps f of 2-spheres S2 with a finite set post(f) of postcritical points.
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph.
Maps close to identity and universal maps in the Newhouse domain
Maps close to identity universal maps Newhouse domain
2010/11/30
Given an n-dimensional Cr-diffeomorphism g, its renormalized iteration is an iteration of g, restricted to a certain n-dimensional ball and taken in some Cr-coordinates in which the ball acquires radi...
An efficient numerical algorithm for the L2 optimal transport problem with applications to image processing
Monge-Amp`ere equation optimal transpor numerical solution
2010/12/14
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method relies on a numerical res...
A view of canonical extension
topological duality canonical extension relational semantics
2010/12/6
This is a short survey illustrating some of the essential as-pects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional op...
The Point Mass Problem on the Real Line
point mass asymptotics orthogonal polynomials point mass asymptotics orthogonal polynomials
2010/12/1
This paper solves the point mass problem on the real line when the recurrence coefficients are asymptotically periodic.First, we give formulae for the perturbed orthogonal polynomi-als and the perturb...
We prove that if Cay(G; S) is a connected Cayley graph with n vertices, and the prime factorization of n is very small, then Cay(G; S) has a hamiltonian cycle. More precisely, if p, q, and r are disti...