Irene Pivotto

activity

20132019

collaborators

4 papers

math.CO2019

Highly-connected planar cubic graphs with few or many Hamilton cycles

Irene Pivotto, Gordon Royle

In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen ("On the numbe…

math.CO2018

Cores of Cubelike Graphs

Laura Mančinska, Irene Pivotto, David E. Roberson +1

A graph is $cubelike$ if it is a Cayley graph for some elementary abelian $2$ -group $Z_{2}^{n}$ . The core of a graph is its smallest subgraph to which it admits a hom…

math.CO2018

Structure of Cubic Lehman Matrices

Dillon Mayhew, Irene Pivotto, Gordon Royle

A pair $(A, B)$ of square $(0, 1)$ -matrices is called a \emph{Lehman pair} if $A B^{T} = J + k I$ for some integer $k \in {- 1, 1, 2, 3, \dots}$ . In this case $A$ and $B$ are called \emph{Lehman…

math.CO2013

Maximum size binary matroids with no AG(3,2)-minor are graphic

Joseph P. S. Kung, Dillon Mayhew, Irene Pivotto +1

We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no AG(3,2)-minor is $(2 r + 1)$ and characterise those matroids achieving this bound. When $r…