Tropical Paths in Vertex-Colored Graphs

  • Johanne Cohen
  • Giuseppe F. Italiano
  • Yannis Manoussakis
  • Kim Thang Nguyen
  • Hong Phong PhamEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10628)


A subgraph of a vertex-colored graph is said to be tropical whenever it contains each color of the initial graph. In this work we study the problem of finding tropical paths in vertex-colored graphs. There are two versions for this problem: the shortest tropical path problem (STPP), i.e., finding a tropical path with the minimum total weight, and the maximum tropical path problem (MTPP), i.e., finding a path with the maximum number of colors possible. We show that both versions of this problems are NP-hard for directed acyclic graphs, cactus graphs and interval graphs. Moreover, we also provide a fixed parameter algorithm for STPP in general graphs and several polynomial-time algorithms for MTPP in specific graphs, including bipartite chain graphs, threshold graphs, trees, block graphs, and proper interval graphs.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Johanne Cohen
    • 1
  • Giuseppe F. Italiano
    • 2
  • Yannis Manoussakis
    • 1
  • Kim Thang Nguyen
    • 3
  • Hong Phong Pham
    • 1
    Email author
  1. 1.LRIUniversity Paris-SaclayOrsayFrance
  2. 2.Department of Civil Engineering and Computer Science EngineeringUniversity of Rome “Tor Vergata”RomeItaly
  3. 3.IBISCUniversity Paris-SaclayEvryFrance

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