17 citations · 17 across the 6 of their papers we have counts for
10 papers
Tree walks and the spectrum of random graphs
Eva-Maria Hainzl, Élie de Panafieu
It is a classic result in spectral theory that the limit distribution of the spectral measure of random graphs G(n, p) converges to the semicircle law in case np tends to infinity…
Robot Positioning Using Torus Packing for Multisets
Chung Shue Chen, Peter Keevash, Sean Kennedy +2
We consider the design of a positioning system where a robot determines its position from local observations. This is a well-studied problem of considerable practical importance an…
Combinatorics of nondeterministic walks
Élie de Panafieu, Michael Wallner
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of…
Exact enumeration of satisfiable 2-SAT formulae
Sergey Dovgal, Élie de Panafieu, Vlady Ravelomanana
We obtain exact expressions counting the satisfiable 2-SAT formulae and describe the structure of associated implication digraphs. Our approach is based on generating function mani…
The birth of the strong components
Sergey Dovgal, Élie de Panafieu, Dimbinaina Ralaivaosaona +2
Random directed graphs undergo a phase transition around the point , and the width of the transition window has been known since the works of Luczak and Seierstad…
2-Xor revisited: satisfiability and probabilities of functions
Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger +1
The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses , is satisfiable. We revisit this classical problem by giving…
Graphs with degree constraints
Élie de Panafieu, Lander Ramos
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This gene…
Enumeration and structure of inhomogeneous graphs
Élie de Panafieu
We analyze a general model of weighted graphs, introduced by de Panafieu and Ravelomanana (2014) and similar to the "inhomogeneous graph model" of Söderberg (2002). Each vertex rec…
Analytic Description of the Phase Transition of Inhomogeneous Multigraphs
Élie de Panafieu, Vlady Ravelomanana
We introduce a new model of random multigraphs with colored vertices and weighted edges. It is similar to the "inhomogeneous random graph model" of Söderberg (2002), extended by Bo…
Phase Transition of Random Non-Uniform Hypergraphs
Elie de Panafieu
Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for a…