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Journal Articles Journal of Combinatorial Optimization Year : 2021

Tropical paths in vertex-colored graphs

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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Dates and versions

hal-03508306 , version 1 (03-01-2022)

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Cite

Johanne Cohen, Giuseppe Italiano, Yannis Manoussakis, Nguyen Kim Thang, Hong Phong Pham. Tropical paths in vertex-colored graphs. Journal of Combinatorial Optimization, 2021, 42 (3), pp.476--498. ⟨10.1007/s10878-019-00416-y⟩. ⟨hal-03508306⟩
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