A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
We generalize the notions of flippable and simultaneously-flippable edges in a triangulation of a set S of points in the plane, into so called pseudo simultaneously-flippable edge...
Michael Hoffmann, Micha Sharir, Adam Sheffer, Csab...
Clustering methods usually require to know the best number of clusters, or another parameter, e.g. a threshold, which is not ever easy to provide. This paper proposes a new graph-b...
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring...
Oleg V. Borodin, Hajo Broersma, Alexei N. Glebov, ...
Given a positive integer n and a family F of graphs, let R(n, F) denote the maximum number of colors in an edge-coloring of Kn such that no subgraph of Kn belonging to F has disti...