7 citations · 19 across the 12 of their papers we have counts for
13 papers
Short rewriting, and geometric explanations related to the active bijection, for: Extension-lifting bijections for oriented matroids, by S. Backman, F. Santos, C.H. Yuen, arXiv:1904.03562v2 (October 29, 2023)
Emeric Gioan
For an oriented matroid M, and given a generic single element extension and a generic single element lifting of M, the main result of [1] provides a bijection between bases of M an…
Rectangles, integer vectors and hyperplanes of the hypercube
E. Gioan, I. P. Silva
We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over and study their properties with respe…
The Active Bijection 2.b - Decomposition of activities for oriented matroids, and general definitions of the active bijection
Emeric Gioan, Michel Las Vergnas
The active bijection for oriented matroids (and real hyperplane arrangements, and graphs, as particular cases) is introduced and investigated by the authors in a series of papers.…
On Tutte polynomial expansion formulas in perspectives of matroids and oriented matroids
Emeric Gioan
We introduce the active partition of the ground set of an oriented matroid perspective (or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by…
Computing the fully optimal spanning tree of an ordered bipolar directed graph
Emeric Gioan, Michel Las Vergnas
It has been previously shown by the authors that a directed graph on a linearly ordered set of edges (ordered graph) with adjacent unique source and sink (bipolar digraph) has a un…
The active bijection for graphs
Emeric Gioan, Michel Las Vergnas
The active bijection forms a package of results studied by the authors in a series of papers in oriented matroids. The present paper is intended to state the main results in the pa…
The Active Bijection 2.a - Decomposition of activities for matroid bases, and Tutte polynomial of a matroid in terms of beta invariants of minors
Emeric Gioan, Michel Las Vergnas
We introduce and study filtrations of a matroid on a linearly ordered ground set, which are particular sequences of nested sets. A given basis can be decomposed into a uniquely def…
On the Number of Circuit-cocircuit Reversal Classes of an Oriented Matroid
Emeric Gioan, Chi Ho Yuen
The first author introduced the circuit-cocircuit reversal system of an oriented matroid, and showed that when the underlying matroid is regular, the cardinalities of such system a…
Orientations of Simplices Determined by Orderings on the Coordinates of their Vertices
Emeric Gioan, Kevin Sol, Gérard Subsol
Provided n points in an (n-1)-dimensional affine space, and one ordering of the points for each coordinate, we address the problem of testing whether these orderings determine if t…
Computation with No Memory, and Rearrangeable Multicast Networks
Serge Burckel, Emeric Gioan, Emmanuel Thomé
We investigate the computation of mappings from a set S^n to itself with "in situ programs", that is using no extra variables than the input, and performing modifications of one co…
Practical and Efficient Circle Graph Recognition
Emeric Gioan, Christophe Paul, Marc Tedder +1
Circle graphs are the intersection graphs of chords in a circle. This paper presents the first sub-quadratic recognition algorithm for the class of circle graphs. Our algorithm is…
Practical and Efficient Split Decomposition via Graph-Labelled Trees
Emeric Gioan, Christophe Paul, Marc Tedder +1
Split decomposition of graphs was introduced by Cunningham (under the name join decomposition) as a generalization of the modular decomposition. This paper undertakes an investigat…
Split decomposition and graph-labelled trees: characterizations and fully-dynamic algorithms for totally decomposable graphs
Emeric Gioan, Christophe Paul
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the dista…