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5 papers · 2 filters
Stack-number is not bounded by queue-number
Vida Dujmović, David Eppstein, Robert Hickingbotham +2
We describe a family of graphs with queue-number at most 4 but unbounded stack-number. This resolves open problems of Heath, Leighton and Rosenberg (1992) and Blankenship and Oporo…
Sparse universal graphs for planarity
Louis Esperet, Gwenaël Joret, Pat Morin
We show that for every integer there exists a graph with vertices and edges such that every -vertex planar graph is isomorphic to a su…
Desargues theorem, its configurations, and the solution to a long-standing enumeration problem
Aiden A. Bruen, Trevor C. Bruen, James M. McQuillan
We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline…
Tight Bounds on the Clique Chromatic Number
Gwenaël Joret, Piotr Micek, Bruce Reed +1
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertices so that no inclusion-wise maximal clique which is not an isolated vertex is mo…
Clustered 3-Colouring Graphs of Bounded Degree
Vida Dujmović, Louis Esperet, Pat Morin +2
A (not necessarily proper) vertex colouring of a graph has "clustering" if every monochromatic component has at most vertices. We prove that planar graphs with maximum degr…