We prove that the geometric thickness of graphs whose maximum degree is no more than four is two. In our proofs, we present a space and time efficient embedding technique for gra...
Christian A. Duncan, David Eppstein, Stephen G. Ko...
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph...
Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines...
Let be a finite building (or, more generally, a thick spherical and locally finite building). The chamber graph G(), whose edges are the pairs of adjacent chambers in , is known t...
Consider the following question: does every complete geometric graph K2n have a partition of its edge set into n plane spanning trees? We approach this problem from three directio...