Dan McQuillan
Norwich University
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Featured researches published by Dan McQuillan.
Discrete Mathematics | 1992
Dan McQuillan; R. Bruce Richter
Abstract In his paper on the crossing numbers of generalized Peterson graphs, Fiorini proves that P(8,3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are interesting in that they focus on disjoint cycles, which must cross each other an even number of times.
Journal of Graph Theory | 1994
Dan McQuillan; R. Bruce Richter
We give a planar proof of the fact that if G is a 3-regular graph minimal with respect to having crossing number at least 2, then the crossing number of G is 2.
Journal of Graph Theory | 2016
Dan McQuillan; R. Bruce Richter
We present several general results about drawings of Kn, as a beginning to trying to determine its crossing number. As application, we give a complete proof that the crossing number of K9 is 36 and that all drawings in one large, natural class of drawings of K11 have at least 100 crossings.
Journal of Combinatorial Theory | 2015
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 Kleitmans parity theorem for the crossing number of K 2 n + 1 combine with a specific drawing of K 13 to show that the crossing number of K 13 is one of the numbers in { 217 , 219 , 221 , 223 , 225 } . We show that the crossing number is not 217.
Journal of Graph Theory | 2018
Alan Arroyo; Dan McQuillan; R. Bruce Richter; Gelasio Salazar
There are three main thrusts to this article: a new proof of Levis Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of
Discrete Mathematics | 2018
Dan McQuillan; James M. McQuillan
K_n
Journal of Combinatorial Theory | 2015
Dan McQuillan; Shengjun Pan; R. Bruce Richter
have
Journal of Combinatorial Theory | 2015
Dan McQuillan; Shengjun Pan; R. Bruce Richter
n^2+{}
College Mathematics Journal | 2014
Dan McQuillan; Rob Poodiack
O
Journal of Combinatorial Theory | 1994
Dan McQuillan; R. Bruce Richter
(n\log n)