Abstract. An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neigh-bourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of colours. This is a widely used subrou-tine for graph isomorphism testing algorithms, since any automorphism needs to be colour preserving. We give an O((m+n) logn) algorithm for finding a canonical version of such a stable colouring, on graphs with n vertices and m edges. We show that no faster algorithm is possible, under some modest assumptions about the type of algorithm, which captures all known colour refinement algorithms.
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easil...
Color refinement is a crucial subroutine in symmetry detection in theory as well as practice. It has...
We show that the following fundamental edge-colouring problem can be solved in polynomial time for a...
Abstract. An assignment of colours to the vertices of a graph is stable if any two vertices of the s...
The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman al...
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a sub-r...
Colour refinement is a simple algorithm that partitions the vertices of a graph according their "ite...
By a proper colouring of a simple graph, we mean an assignment of colours to its vertices with adjac...
AbstractIt is well known that the problem of graph k-colourability, for any k≥3, is NP-complete but ...
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order ...
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order ...
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c: V → {1, 2,..., k} such ...
AbstractWe study colourings of graphs with the property that the number of used colours cannot be re...
Abstract. The performance guarantee of a graph coloring algorithm is the worst case ratio between th...
International audienceIn this paper we consider a variation of a recoloring problem, called the r-Co...
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easil...
Color refinement is a crucial subroutine in symmetry detection in theory as well as practice. It has...
We show that the following fundamental edge-colouring problem can be solved in polynomial time for a...
Abstract. An assignment of colours to the vertices of a graph is stable if any two vertices of the s...
The Colour Refinement procedure and its generalisation to higher dimensions, the Weisfeiler-Leman al...
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a sub-r...
Colour refinement is a simple algorithm that partitions the vertices of a graph according their "ite...
By a proper colouring of a simple graph, we mean an assignment of colours to its vertices with adjac...
AbstractIt is well known that the problem of graph k-colourability, for any k≥3, is NP-complete but ...
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order ...
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order ...
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c: V → {1, 2,..., k} such ...
AbstractWe study colourings of graphs with the property that the number of used colours cannot be re...
Abstract. The performance guarantee of a graph coloring algorithm is the worst case ratio between th...
International audienceIn this paper we consider a variation of a recoloring problem, called the r-Co...
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easil...
Color refinement is a crucial subroutine in symmetry detection in theory as well as practice. It has...
We show that the following fundamental edge-colouring problem can be solved in polynomial time for a...