A simple characterization of the 3, 4, or 5-colorable Eulerian triangulations of the projective plane is given. Key words: Projective plane, triangulation, coloring, Eulerian grap...
A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
We show that the vertices of any plane graph in which every face is of length at least g can be colored by (3g - 5)/4 colors so that every color appears in every face. This is nea...
Noga Alon, Robert Berke, Kevin Buchin, Maike Buchi...
A graph is terminal ∆ − Y -reducible if, it can be reduced to a distinguished set of terminal vertices by a sequence of series-parallel reductions and ∆−Y -transformations...
Existing geographic routing algorithms depend on the planarization of the network connectivity graph for correctness, and the planarization process gives rise to a welldefined no...