Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

W. Zane Billings; Justin Clifton; Josh Hiller; Tommy Meek; Andrew Penland; Wesley Rogers; Gabriella Smokovich; Andrew Vasquez-Berroteran; Eleni Zamagias

Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

Combinatorics 2020-03-03 v1

Authors: W. Zane Billings , Justin Clifton , Josh Hiller , Tommy Meek , Andrew Penland , Wesley Rogers , Gabriella Smokovich , Andrew Vasquez-Berroteran , Eleni Zamagias

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Abstract

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.

Keywords

ramsey theory and colorings

Cite

@article{arxiv.2003.00035,
  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 preprint arXiv:2003.00035},
  year   = {2020}
}

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12 pages

Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

Abstract

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