Skip to main content
Article thumbnail
Location of Repository

Obtaining online ecological colourings by generalizing first-fit.

By M. Johnson, V. Patel, Daniel Paulusma and T. Trunck


A colouring of a graph is ecological if every pair of vertices that have the same set of colours in their neighbourhood are coloured alike. We consider the following problem: if a graph G and an ecological colouring c of G are given, can further vertices added to G, one at a time, be coloured using colours from some finite set C so that at each stage the current graph is ecologically coloured? If the answer is yes, then we say that the pair (G,c) is ecologically online extendible. By generalizing the well-known First-Fit algorithm, we are able to characterize when (G,c) is ecologically online extendible. For the case where c is a colouring of G in which each vertex is coloured distinctly, we give a simple characterization of when (G,c) is ecologically online extendible using only the colours of c, and we also show that (G,c) is always online extendible if we permit ourselves to use one extra colour. We also study (off-line) ecological H-colourings where the colouring must satisfy further restrictions imposed by some fixed pattern graph H. We characterize the computational complexity of this problem. This solves an open question posed by Crescenzi et al

Publisher: Springer
Year: 2010
DOI identifier: 10.1007/978-3-642-13182-0_22
OAI identifier:

Suggested articles


  1. (1998). Coloring graphs on-line. In: Online algorithms: the state of the art
  2. (1994). Ecological and perfect colorings,
  3. (1992). Graph colorings and power in experimental exchange networks,
  4. (1990). On the complexity of H-colouring,
  5. (2008). On the existence of Ecological Colouring,
  6. (1988). On-line and first-fit colorings of graphs.
  7. (1991). Role colouring a graph,
  8. (1993). Social networks as normal science,
  9. (1991). STRUCTURE Version 4.2 Reference Manual, Center for the Social Sciences,
  10. (1988). The relational basis of attitudes, Social Structures: A Network Approach, Cambridge,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.