Linear transformations between colorings in chordal graphs

by   Nicolas Bousquet, et al.
Grenoble Institute of Technology

Let k and d be such that k > d+2. Consider two k-colorings of a d-degenerate graph G. Can we transform one into the other by recoloring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. If k=d+2, we know that there exists graphs for which a quadratic number of recolorings is needed. And when k=2d+2, there always exists a linear transformation. In this paper, we prove that, as long as k > d+4, there exists a transformation of length at most f(Δ) · n between any pair of k-colorings of chordal graphs (where Δ denotes the maximum degree of the graph). The proof is constructive and provides a linear time algorithm that, given two k-colorings c_1,c_2 computes a linear transformation between c_1 and c_2.


page 1

page 2

page 3

page 4


Recoloring graphs of treewidth 2

Two (proper) colorings of a graph are adjacent if they differ on exactly...

Short and local transformations between (Δ+1)-colorings

Recoloring a graph is about finding a sequence of proper colorings of th...

Accretive Computation of Global Transformations of Graphs

The framework of global transformations aims at describing synchronous r...

Digraph redicolouring

Given two k-dicolourings of a digraph D, we prove that it is PSPACE-comp...

Paths between colourings of sparse graphs

The reconfiguration graph R_k(G) of the k-colourings of a graph G has as...

Centralised Connectivity-Preserving Transformations by Rotation: 3 Musketeers for all Orthogonal Convex Shapes

We study a model of programmable matter systems consisting of n devices ...

The Alternating BWT: an algorithmic perspective

The Burrows-Wheeler Transform (BWT) is a word transformation introduced ...

Please sign up or login with your details

Forgot password? Click here to reset