277 citations
- University of California, BerkeleyUS7 papers
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- Brookhaven National LaboratoryUS6 papers
- Lancaster UniversityGB6 papers
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- LIP - Laboratory of Instrumentation and Experimental Particle PhysicsPT6 papers
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4 papers · 1 filter
Drawings of complete graphs in the projective plane
Alan Arroyo, Dan McQuillan, R. Bruce Richter +2
Hill's Conjecture states that the crossing number of the complete graph in the plane (equivalently, the sphere) is $\frac{1}{4}\lfloor\frac{n}{2}\rfloor\lflo…
Convex drawings of the complete graph: topology meets geometry
Alan Arroyo, Dan McQuillan, R. Bruce Richter +1
In this work, we introduce and develop a theory of convex drawings of the complete graph in the sphere. A drawing of is convex if, for every 3-cycle of , t…
Levi's Lemma, pseudolinear drawings of , and empty triangles
Alan Arroyo, Dan McQuillan, Bruce Richter +1
There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudoline…
On the crossing number of K_13
Dan McQuillan, Shengjun Pan, R. Bruce Richter
Since the crossing number of K_{12} is now known to be 150, it is well-known that simple counting arguments and Kleitman's parity theorem for the crossing number of K_{2n+1} combin…