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- Publications
- Influence

Even Cycle and Even Cut Matroids

- I. Pivotto
- Mathematics
- 20 May 2011

In this thesis we consider two classes of binary matroids, even cycle matroids and even cut matroids. They are a generalization of graphic and cographic matroids respectively. We focus on two main… Expand

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When does a biased graph come from a group labelling?

- M. DeVos, Daryl Funk, I. Pivotto
- Mathematics, Computer Science
- Adv. Appl. Math.
- 29 March 2014

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

Biased graphs with no two vertex-disjoint unbalanced cycles

- Rong Chen, I. Pivotto
- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 8 March 2014

Lov\'asz 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-disjoint odd… Expand

Packing Steiner trees

- M. DeVos, J. McDonald, I. Pivotto
- Computer Science, Mathematics
- J. Comb. Theory, Ser. B
- 29 July 2013

Let T be a distinguished subset of vertices in a graph G. A T-Steiner tree is a subgraph of G that is a tree and that spans T. Kriesell conjectured that G contains k pairwise edge-disjoint T-Steiner… Expand

Relationships between Pairs of Representations of Signed Binary Matroids

- Bertrand Guenin, Irene Pivotto, Paul Wollan
- Computer Science, Mathematics
- SIAM J. Discret. Math.
- 12 February 2013

We show how pairs of signed graphs with the same even cycles relate to pairs of grafts with the same even cuts. These results are proved in the more general context of signed binary matroids.

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

- Irene Pivotto, Gordon A. Royle
- Mathematics, Computer Science
- Discret. Math.
- 30 January 2019

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 number of longest and… Expand

3-Flows with large support

- M. DeVos, J. McDonald, I. Pivotto, Edita Rollová, R. Sámal
- Computer Science, Mathematics
- J. Comb. Theory, Ser. B
- 25 January 2017

We prove that every 3-edge-connected graph $G$ has a 3-flow $\phi$ with the property that $|\mathop{supp}(\phi)| \ge \frac{5}{6} |E(G)|$. The graph $K_4$ demonstrates that this $\frac{5}{6}$ ratio is… Expand

Highly contrasted responses of Mediterranean octocorals to climate change along a depth gradient

- I. Pivotto, D. Nérini, M. Masmoudi, H. Kara, L. Chaoui, D. Aurelle
- Medicine, Biology
- Royal Society Open Science
- 1 May 2015

Climate change has a strong impact on marine ecosystems, including temperate species. Analysing the diversity of thermotolerance levels within species along with their genetic structure enables a… Expand

Stabilizer theorems for even cycle matroids

- Bertrand Guenin, Irene Pivotto, Paul Wollan
- Mathematics, Computer Science
- J. Comb. Theory, Ser. B
- 1 May 2016

A signed graph is a representation of an even cycle matroid M if the cycles of M correspond to the even cycles of that signed graph. Two long standing open questions regarding even cycle matroids are… Expand

Maximum Size Binary Matroids with no AG(3, 2)-Minor are Graphic

- J. Kung, D. Mayhew, I. Pivotto, G. Royle
- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 9 April 2013

We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no $AG(3,2)$-minor is $\binom{r+1}{2}$ and characterize those matroids achieving this bound. When $r \geq 6$, the g...