Brigitte Chauvin Knihy

This work covers a range of topics in graph theory, combinatorics, and random processes. It includes discussions on colored maps and trees, limit laws for lattice paths, and counting walks in the quarter plane. The text explores bijective constructions of equivalent ecosystems and examines the random boundary of planar maps. It also delves into the enumeration of 2-trees and the relationship between breadth-first search, triangle-free graphs, and Brownian motion. The study of random planar lattices and integrated super-Brownian excursions is presented, alongside investigations into the diameter of long-range percolation graphs and giant components in expanding graph processes. The work addresses coloring random graphs from an algorithmic perspective and identifies a sharp threshold for non-monotone digraph properties. It discusses the approximability of path coloring problems in mesh and torus networks and minimal spanning trees with random edge lengths. Additional topics include generalized pattern matching statistics, random suffix search trees, and the profile of random forests. The analysis of heap construction costs, combinatorial problems in information theory, and the distribution of sizes of simplified trees are also featured. The text concludes with insights into random walks in random environments, convergence rates for stable weighted branching processes, and cooperative approaches to various problems in graph theo