Crossing

Crossing technique in cowpeas

Non-Crossing Frameworks with Non-Crossing Reciprocals

We study non-crossing frameworks in the plane for which the classical reciprocal on the dual graph is also non-crossing. We give a complete description of the self-stresses on non-crossing frameworks G whose reciprocals are non-crossing, in terms of: the types of faces (only pseudo-triangles and pseudo-quadrangles are allowed); the sign patterns in the stress on G; and a geometric condition on ...

Odd Crossing Number Is Not Crossing Number

The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbe...

Crossing number, pair-crossing number, and expansion

The crossing number crðGÞ of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcrðGÞ is the smallest number of pairs of edges that cross in a drawing of G in the plane. While crðGÞXpcrðGÞ holds trivially, it is not known whether a strict inequality can ever occur (this question was raised by Mohar and Pach and Tóth). We ai...

Crossing the threshold of Iranian TEFL

Teaching  English  in  an  Iranian  and  Islamic  culture  poses  complex  questions  for  both  teachers and learners. In this paper, the authors intend to shed light on what it means to teach English as a  foreign  language  (TEFL)  in  an  Islamic-Iranian  context.  Having  reviewed  the  colonial  and postmodern views of English language teaching, the authors took a look beyond the current ...