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- Pierre Aboulker, Marko Radovanovic, Nicolas Trotignon, Kristina Vuskovic
- SIAM J. Discrete Math.
- 2012

We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes of graphs that do not contain as a subgraph and as an induced subgraph, a cycle with a node that has at least two… (More)

We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs… (More)

A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We prove that every graph that does not contain a wheel as a subgraph is 3-colorable. Résumé : Une roue est un graph formé d'un cycle… (More)

- Pierre Aboulker, Marko Radovanovic, Nicolas Trotignon, Théophile Trunck, Kristina Vuskovic
- Journal of Graph Theory
- 2014

In [Structural properties and decomposition of linear balanced matrices , Mathematical Programming, 55:129–168, 1992], Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear… (More)

- Pierre Aboulker, John Adrian Bondy, Xiaomin Chen, Ehsan Chiniforooshan, Vasek Chvátal, Peihan Miao
- Discrete Applied Mathematics
- 2014

- Pierre Aboulker, Maria Chudnovsky, Paul D. Seymour, Nicolas Trotignon
- Eur. J. Comb.
- 2015

A wheel is a graph formed by a chordless cycle C and a vertex u not in C that has at least three neighbors in C. We prove that every 3-connected planar graph that does not contain a wheel as an induced subgraph is either a line graph or has a clique cutset. We prove that every planar graph that does not contain a wheel as an induced subgraph is 3-colorable.… (More)

- Pierre Aboulker, Rohan Kapadia
- Eur. J. Comb.
- 2015

A classical theorem of Euclidean geometry asserts that any non-collinear set of n points in the plane determines at least n distinct lines. Chen and Chvátal conjectured a generalization of this result to arbitrary finite metric spaces, with a particular definition of lines in a metric space. We prove it for metric spaces induced by connected… (More)

- Pierre Aboulker, Xiaomin Chen, Guangda Huzhang, Rohan Kapadia, Cathryn Supko
- Discrete & Computational Geometry
- 2016

- Pierre Aboulker, Jørgen Bang-Jensen, +4 authors José Zamora
- ArXiv
- 2016

- Pierre Aboulker, Zhentao Li, Stéphan Thomassé
- Electronic Notes in Discrete Mathematics
- 2015