Partial convex recolorings of trees and galled networks: Tight upper and lower bounds

Shlomo Moran, Sagi Snir, Wing Kin Sung

Research output: Contribution to journalArticlepeer-review


A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. When a coloring of a graph is not convex, a natural question is how far it is from a convex one. This problem is denoted as convex recoloring (CR).While the initial works on CR defined and studied the problem on trees, recent efforts aim at either generalizing the underlying graphs or specializing the input colorings. In this work, we extend the underlying graph and the input coloring to partially colored galled networks. We show that although determining whether a coloring is convex on an arbitrary network is hard, it can be found efficiently on galled networks. We present a fixed parameter tractable algorithm that finds the recoloring distance of such a network whose running time is quadratic in the network size and exponential in that distance. This complexity is achieved by amortized analysis that uses a novel technique for contracting colored graphs that seems to be of independent interest.

Original languageEnglish
Article number42
JournalACM Transactions on Algorithms
Issue number4
StatePublished - Sep 2011


  • Convex recoloring
  • NP-hardness
  • Partially colored galled networks
  • Partially colored trees

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


Dive into the research topics of 'Partial convex recolorings of trees and galled networks: Tight upper and lower bounds'. Together they form a unique fingerprint.

Cite this