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.
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Funding was provided by DS0704 Fondements du numérique - 2015 (Grant No. ANR-15-CE40-0015).
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Cohen, J., Italiano, G.F., Manoussakis, Y. et al. Tropical paths in vertex-colored graphs. J Comb Optim 42, 476–498 (2021). https://doi.org/10.1007/s10878-019-00416-y
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DOI: https://doi.org/10.1007/s10878-019-00416-y