• Corpus ID: 211678009

Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles.

@article{Billings2020AvoidingMS,
  title={Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles.},
  author={W. Zane Billings and Justin Clifton and Josh Hiller and Tommy Meek and Andrew Penland and Wesley Rogers and Gabriella Smokovich and Andrew Vasquez-Berroteran and Eleni Zamagias},
  journal={arXiv: Combinatorics},
  year={2020}
}
We present a recursive formula for the number of ways to color $j$ vertices blue in an r-uniform hyperpath of size $n$ while avoiding a blue monochromatic sub-hyperpath of length k. We use this result to solve the corresponding problem for $(r-1)$-tight r-uniform paths and loose r-uniform cycles. This generalizes some well known results from reliability engineering and analysis. 

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