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Tropical paths in vertex-colored graphs

Author

Listed:
  • Johanne Cohen

    (University Paris-Saclay)

  • Giuseppe F. Italiano

    (University of Rome “Tor Vergata”)

  • Yannis Manoussakis

    (University Paris-Saclay)

  • Nguyen Kim Thang

    (University Paris-Saclay)

  • Hong Phong Pham

    (University Paris-Saclay)

Abstract

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.

Suggested Citation

  • Johanne Cohen & Giuseppe F. Italiano & Yannis Manoussakis & Nguyen Kim Thang & Hong Phong Pham, 0. "Tropical paths in vertex-colored graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-23.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-019-00416-y
    DOI: 10.1007/s10878-019-00416-y
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