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math.CO2022
A Note on the Number of Regions in a Line Arrangement
Dickson Y. B. Annor, Michael S. Payne
For an arrangement of lines in the real projective plane, we denote by the number of regions into which the real projective plane is divided by the lines. Using Bojanowski'…
math.CO2020
Intersecting longest paths in chordal graphs
Daniel J. Harvey, Michael S. Payne
We consider the size of the smallest set of vertices required to intersect every longest path in a chordal graph. Such sets are known as longest path transversals. We show that if…
math.CO2015
Bichromatic lines in the plane
Michael S. Payne
Given a set of red and blue points in the plane, a bichromatic line is a line containing at least one red and one blue point. We prove the following conjecture of Kleitman and Pinc…