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) and the tropical path problem (TPP). We show that two problem versions are NP-hard for DAG graphs, cactus graphs and interval graphs. Moreover, we also provides a dynamic programming algorithm for STPP and prove polynomial algorithms for TPP for some specific graphs including trees, block graphs bipartite chain graphs and threshold graphs. Throughout the paper we left some open questions.
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https://hal.archives-ouvertes.fr/hal-01635425
Contributor : Johanne Cohen <>
Submitted on : Wednesday, November 15, 2017 - 10:48:15 AM
Last modification on : Wednesday, January 23, 2019 - 1:48:04 PM

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Johanne Cohen, Giuseppe F. Italiano, Yannis Manoussakis, Nguyen Kim Thang, Phong Pham, et al.. Tropical paths in vertex-colored graphs. COCOA 2017 - 11th Annual International Conference on Combinatorial Optimization and Applications, Dec 2017, Shangai, China. pp.291-305, ⟨10.1007/978-3-319-71147-8_20⟩. ⟨hal-01635425⟩

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