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Maximum Colorful Cycles in Vertex-Colored Graphs

  • Giuseppe F. Italiano
  • Yannis Manoussakis
  • Nguyen Kim Thang
  • Hong Phong PhamEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10846)

Abstract

In this paper, we study the problem of finding a maximum colorful cycle a vertex-colored graph. Specifically, given a graph with colored vertices, the goal is to find a cycle containing the maximum number of colors. We aim to give a dichotomy overview on the complexity of the problem. We first show that the problem is NP-hard even for simple graphs such as split graphs, biconnected graphs, interval graphs. Then we provide polynomial-time algorithms for classes of vertex-colored threshold graphs and vertex-colored bipartite chain graphs, which are our main contributions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Giuseppe F. Italiano
    • 2
  • Yannis Manoussakis
    • 1
  • Nguyen Kim Thang
    • 3
  • Hong Phong Pham
    • 1
    Email author
  1. 1.LRIUniversity Paris-SaclayOrsayFrance
  2. 2.University of Rome Tor VergataRomeItaly
  3. 3.IBISCUniversity Paris-SaclayEvryFrance

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