48 citations · 123 across the 22 of their papers we have counts for
33 papers
A Schnyder-type drawing algorithm for 5-connected triangulations
Olivier Bernardi, Éric Fusy, Shizhe Liang
We define some Schnyder-type combinatorial structures on a class of planar triangulations of the pentagon which are closely related to 5-connected triangulations. The combinatorial…
Grand Schnyder Woods
Olivier Bernardi, Éric Fusy, Shizhe Liang
We define a far-reaching generalization of Schnyder woods which encompasses many classical combinatorial structures on planar graphs. Schnyder woods are defined for planar triangul…
Tutte polynomials for regular oriented matroids
Jordan Awan, Olivier Bernardi
The Tutte polynomial is a fundamental invariant of graphs and matroids. In this article, we define a generalization of the Tutte polynomial to oriented graphs and regular oriented…
Universal Tutte polynomial
Olivier Bernardi, Tamas Kalman, Alex Postnikov
The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polyma…
Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function
Olivier Bernardi, Philippe Nadeau
Let G be a graph, and let G be its chromatic polynomial. For any non-negative integers i, j, we give an interpretation for the evaluation (i) G (--j) in terms of acyclic ori…
Percolation on triangulations: a bijective path to Liouville quantum gravity
Olivier Bernardi, Nina Holden, Xin Sun
We set the foundation for a series of works aimed at proving strong relations between uniform random planar maps and Liouville quantum gravity (LQG). Our method relies on a bijecti…