What question did this study set out to answer?

This study aims to classify the complexity of finding quasi-Hamiltonian paths with constraints on vertex coverage from color classes in multipartite digraphs.

July 6, 2026Discrete Applied MathematicsOpen Access

The complexity of color-constrained paths in semicomplete multipartite digraphs

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This study aims to classify the complexity of finding quasi-Hamiltonian paths with constraints on vertex coverage from color classes in multipartite digraphs.
Analyzing quasi-Hamiltonian path problems with prescribed start and end vertices.
Utilizing Schaefer's dichotomy theorem to classify the complexity of path problems.
Generalizing sufficient criteria for Hamiltonian paths to sufficient criteria for quasi-Hamiltonian paths.
Identified that the quasi-Hamiltonian path problem with specific color vertex constraints is NP-complete.
Provided initial results suggesting potential for polynomial-time solvability in restricted cases.
Classified the complexity of almost all related problems within the framework established.

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This research investigates color-constrained paths in semicomplete multipartite digraphs, indicating complexity of various path problems.

Cite This Study

Julian Brinkmann (2026) studied this question.

synapsesocial.com/papers/6a4b44fa997070ff83b5aea9 https://doi.org/10.1016/j.dam.2026.06.030

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The complexity of color-constrained paths in semicomplete multipartite digraphs

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Implication

Cite This Study

The complexity of color-constrained paths in semicomplete multipartite digraphs

Key Points

Discussion

Implication

Cite This Study

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