5 papers
All-angles bisection of polygon area
Robin Whitty
Given a simple polygon we aim to find the equation of the straight line which bisects the area of the polygon in a given direction. Additionally, we would like to vary this directi…
Bisecting a triangle in a given direction
Robin Whitty
Given a triangle, what is the equation of the line which bisects its area and has a given slope? The set of all lines bisecting the area of a triangle has been elegantly determined…
An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations
Carrie Rutherford, Robin Whitty
A fundamental theorem of matroid theory establishes that a transversal matroid is representable over fields of any characteristic. It was proved in 1970 by Piff and Welsh: their pr…
Some Comments on Multiple Discovery in Mathematics
Robin Whitty
Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong…
Pancyclicity when each cycle must pass exactly Hamilton cycle chords
Fatima Affif Chaouche, Carrie Rutherford, Robin Whitty
It is known that chords must be added to an -cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, $Θ(n…