We prove that a graph is 4-colorable if and only if it can be drawn with vertices in the integer lattice, using as edges only line segments not containing a third point of the lattice.

We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A; B 2 O are called visible if there exist points x 2 A; y 2 B such that x is visible from y. We consider visibility only for a nite set...

The Department of Archaeology at Siena has been engaged for several decades in the testing of new methodologies, new approaches and new instruments for construction of the archaeological record. In relation to landscape archaeology and in particular with the South Tuscan landscapes the low level of visibility and heavy clay soils have directed us towards those techniques of remote sensing that ...

Land-cover and climate change are both expected to alter species distributions and contribute to future biodiversity loss. However, the combined effects of land-cover and climate change on assemblages, especially at the landscape scale, remain understudied. Lowland tropical amphibians may be particularly susceptible to changes in land cover and climate warming because many species have narrow t...

We show that every segment endpoint visibility graph on disjoint line segments in the plane admits an alternating path of length , answering a question of Bose. This bound is optimal apart from a constant factor. We also give bounds on the constants hidden by the asymptotic notation.

The monitoring of earth surface dynamic processes at a global scale requires high temporal frequency remote sensing observations which are provided up to now by moderate spatial resolution sensors. However, the spatial heterogeneity within the moderate spatial resolution pixel biases non-linear estimation processes of land surface variables from remote sensing data. To limit its influence on th...

This article studies the visibility of creative acts and how the aesthetic experience of future architectural form can be seen in movements of the hands, in concert with speech and bodily conduct. Selected sequences are studied closely in two settings to examine the ways that our human interactional practices organise the depiction of architectural concepts and spaces, which can then be explore...