2 citations · 2 across the 5 of their papers we have counts for
7 papers
Design spectra for 6-regular graphs with 12 vertices
Anthony D. Forbes, Carrie G. Rutherford
The design spectrum of a simple graph is the set of positive integers such that there exists an edgewise decomposition of the complete graph into $n(n - 1)/(2 |E(G)|)…
Generalized pentagonal geometries
Anthony D. Forbes, Carrie G. Rutherford
A pentagonal geometry PENT(, ) is a partial linear space, where every line is incident with points, every point is incident with lines, and for each point , there…
Mixing Time of Markov chain of the Knapsack Problem
Koko K. Kayibi, S. Pirzada, Carrie Rutherford
To find the number of assignments of zeros and ones satisfying a specific Knapsack Problem is hard, so only approximations are envisageable. A Markov chain allowing uniform s…
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 results on the structure and spectra of matrix-products
Murad Banaji, Carrie Rutherford
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structu…
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…
P-matrices and signed digraphs
Murad Banaji, Carrie Rutherford
We associate a signed digraph with a list of matrices whose dimensions permit them to be multiplied, and whose product is square. Cycles in this graph have a parity, that is, they…