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math.CO2016
Proper Orientations of Planar Bipartite Graphs
Fiachra Knox, Sebastián González Hermosillo de la Maza, Bojan Mohar +1
An orientation of a graph is proper if any two adjacent vertices have different indegrees. The proper orientation number of a graph is the minimum of…
math.CO2016
The crossing number of the cone of a graph
Carlos A. Alfaro, Alan Arroyo, Marek Derunár +1
Motivated by a problem asked by Richter and by the long standing Harary-Hill conjecture, we study the relation between the crossing number of a graph and the crossing number of…
math.CO2016
Planar digraphs of digirth four are 2-colourable
Zhentao Li, Bojan Mohar
Neumann-Lara conjectured in 1985 that every planar digraph with digirth at least three is 2-colourable, meaning that the vertices can be 2-coloured without creating any monochromat…