Irene Pivotto

activity

20112019

most citedIsomorphism for even cycle matroids - I

1 citations · 3 across the 9 of their papers we have counts for

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13 papers · 1 filter

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.CO2017★ 1 cited

3-Flows with Large Support

Matt DeVos, Jessica McDonald, Irene Pivotto +2

We prove that every 3-edge-connected graph $G$ has a 3-flow $ϕ$ with the property that $∣ s u pp (ϕ) ∣ \geq \frac{5}{6} ∣ E (G) ∣$ . The graph $K_{4}$ demonstrates that this $\frac{5}…

math.CO2016

Matrix representations of frame and lifted-graphic matroids correspond to gain functions

Daryl Funk, Irene Pivotto, Daniel Slilaty

Let $M$ be a 3-connected matroid and let $F$ be a field. Let $A$ be a matrix over $F$ representing $M$ and let $(G, B)$ be a biased graph representing $M$ .…

math.CO2016★ 1 cited

The circular altitude of a graph

John Bamberg, Brian Corr, Alice Devillers +3

In this paper we investigate a parameter of graphs, called the circular altitude, introduced by Peter Cameron. We show that the circular altitude provides a lower bound on the circ…

math.CO2015

On excluded minors of connectivity 2 for the class of frame matroids

Matt DeVos, Daryl Funk, Irene Pivotto

We investigate the set of excluded minors of connectivity 2 for the class of frame matroids. We exhibit a list $E$ of 18 such matroids, and show that if $N$ is such an ex…

math.CO2014

Graphical representations of graphic frame matroids

Rong Chen, Matt DeVos, Daryl Funk +1

A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame ma…

math.CO2014

When does a biased graph come from a group labelling?

Matt DeVos, Daryl Funk, Irene Pivotto

A biased graph consists of a graph $G$ together with a collection of distinguished cycles of $G$ , called balanced cycles, with the property that no theta subgraph contains exactly…

math.CO2014

Biased graphs with no two vertex-disjoint unbalanced cycles

Rong Chen, Irene Pivotto

Lovász has completely characterised the structure of graphs with no two vertex-disjoint cycles, while Slilaty has given a structural characterisation of graphs with no two vertex-d…

math.CO2013

Packing Steiner Trees

Matt DeVos, Jessica McDonald, Irene Pivotto

Let $T$ be a distinguished subset of vertices in a graph $G$ . A $T$ -\emph{Steiner tree} is a subgraph of $G$ that is a tree and that spans $T$ . Kriesell conjectured that $G$ contai…

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…

math.CO2011★ 1 cited

Isomorphism for even cycle matroids - I

Bertrand Guenin, Irene Pivotto, Paul Wollan

A seminal result by Whitney describes when two graphs have the same cycles. We consider the analogous problem for even cycle matroids. A representation of an even cycle matroid is…