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2020

2020

We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number k ≥ 0 of hamiltonian cycles…

2020

2020

The disproved Nash-Williams conjecture states that every 4-regular 4-connected graph has a hamiltonian cycle. We show that a…

2019

2019

It is conjectured that within the class group of any number field, for every integer $\ell \geq 1$, the $\ell$-torsion subgroup…

2016

2016

NSF [DMS-1302886, DMS-1201374]; Prometeo/Generalitat Valenciana [MTM2013-40464-P]; Simons Foundation Fellowship [305247]

2015

2015

Let $$({\mathcal {A}},{\mathcal {A}}',{\mathcal {A}}^H)$$(A,A′,AH) be the triple of hyperplane arrangements. We show that the…

Review

2014

Review

2014

Many real-world phenomena can be modelled using networks. Often, these networks interact with one another in non-trivial ways…

2013

2013

In 1995, Paul Erdos and Andras Gyarfas conjectured that for every graph of minimum degree at least 3, there exists a non-negative…

2012

2012

In this work in common with Daniele Faenzi we describe the logarithmic bundle associated to a arrangement of lines in P(C) as the…

2010

2010

Abstract We give a concise exposition of the elegant proof given recently by Leonid Gurvits for several lower bounds on…

2009

2009

The Segre-Gimigliano-Harbourne-Hirschowitz Conjecture can be naturally formulated for Hirzebruch surfaces $${\mathbb{F}_n}$$. We…