# Fixed-Parameter Tractability of Maximum Colored Path and Beyond

@article{Fomin2022FixedParameterTO, title={Fixed-Parameter Tractability of Maximum Colored Path and Beyond}, author={F. Fomin and Petr A. Golovach and Tuukka Korhonen and Kirill Simonov and Giannos Stamoulis}, journal={ArXiv}, year={2022}, volume={abs/2207.07449} }

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as follows. We give a randomized algorithm, that given a colored n-vertex undirected graph, vertices s and t, and an integer k, finds an (s, t)-path containing at least k different colors in time 2knO(1). This is the first FPT algorithm for this problem, and it…

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