We consider a robust variant of Dirac-type problems in $k$-uniform hypergraphs. For instance, we prove that if $\mathcal{H}$ is hypergraph with minimum codegree at least $\left(\frac 12 + \gamma \right)n$, $\gamma >0$, and $n$ sufficiently large, then any edge coloring $\phi$ satisfying appropriate local constraints yields properly colored tight Hamilton cycle $\mathcal{H}$. Similar results ...

Minimalist grammars (MGs) constitute a mildly contextsensitive formalism when being equipped with a particular locality condition (LC), the shortest move condition. In this format MGs define the same class of derivable string languages as multiple context-free grammars (MCFGs). Adding another LC to MGs, the specifier island condition (SPIC), results in a proper subclass of derivable languages. ...

For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same color. We show that the proper-walk connection number is at most three for all cyclic graphs, and at most two for bridgeless graphs. We also characterize the bi...

In this short paper, we apply estimates and ideas from [CM4] to study the ends of a properly embedded complete minimal surface 2 ⊂ R3 with finite topology. The main result is that any complete properly embedded minimal annulus that lies above a sufficiently narrow downward sloping cone must have finite total curvature. In this short paper, we apply estimates and ideas from [CM4] to study the en...

This note is meant to clarify the relation between different commonly used definitions of proper discontinuity without the local compactness assumption for the underlying topological space. Much of the discussion applies to actions of nondiscrete topological groups, but, since my primary interest is geometric group theory, I will work only with discrete groups. Throughout this note, I will be w...

In this paper we show that bending a finite volume hyperbolic d-manifold M along a totally geodesic hypersurface Σ results in a properly convex projective structure on M with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We then use this result to show in each dimension d Ê 3 there are examples finite volume, ...