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Dive into the research topics where Dan McQuillan is active.

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Featured researches published by Dan McQuillan.


Discrete Mathematics | 1992

On the crossing numbers of certain generalized Petersen graphs

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

On 3-regular graphs having crossing number at least 2

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

On the Crossing Number of Kn without Computer Assistance

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

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 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

Levi's Lemma, pseudolinear drawings of Kn, and empty triangles

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

Strong vertex-magic and edge-magic labelings of 2-regular graphs of odd order using Kotzig completion

Dan McQuillan; James M. McQuillan

K_n


Journal of Combinatorial Theory | 2015

On the crossing number of K13

Dan McQuillan; Shengjun Pan; R. Bruce Richter

have


Journal of Combinatorial Theory | 2015

On the crossing number of K13K13

Dan McQuillan; Shengjun Pan; R. Bruce Richter

n^2+{}


College Mathematics Journal | 2014

On the Differentiation Formulae for Sine, Tangent, and Inverse Tangent

Dan McQuillan; Rob Poodiack

O


Journal of Combinatorial Theory | 1994

Equality in a result of Kleitman

Dan McQuillan; R. Bruce Richter

(n\log n)

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James M. McQuillan

Western Illinois University

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Alan Arroyo

University of Waterloo

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Gelasio Salazar

Universidad Autónoma de San Luis Potosí

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