Guillem Perarnau

Fast recoloring of sparse graphs

In this paper, we show that for every graph of maximum average degree bounded away from

On the tree-depth of random graphs

d

ON THE RELATION BETWEEN GRAPH DISTANCE AND EUCLIDEAN DISTANCE IN RANDOM GEOMETRIC GRAPHS

, any

LARGE SUBGRAPHS WITHOUT SHORT CYCLES

(d+1)

A probabilistic approach to consecutive pattern avoiding in permutations

-coloring can be transformed into any other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. In particular, it implies that we can transform any

Counting independent sets in cubic graphs of given girth

8

How to Determine if a Random Graph with a Fixed Degree Sequence Has a Giant Component

-coloring of a planar graph into any other

Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting

8

Acyclic edge colourings of graphs with large girth

-coloring with a polynomial number of recolorings. These results give some evidence on a conjecture of Cereceda, van den Heuvel and Johnson which asserts that any

Rainbow Matchings: existence and counting☆

(d+2)