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Rainbow Threshold Graphs

Combinatorics 2025-04-16 v2

Abstract

We define a generalization of threshold graphs which we call kk-rainbow threshold graphs. We show that the collection of kk-rainbow threshold graphs do not satisfy the 00-11 law for first order logic and that asymptotically almost surely all (k+1)(k+1)-rainbow threshold graphs are not isomorphic to a kk-rainbow threshold graph.

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Cite

@article{arxiv.2504.09399,
  title  = {Rainbow Threshold Graphs},
  author = {Nathanael Ackerman and Mostafa Mirabi},
  journal= {arXiv preprint arXiv:2504.09399},
  year   = {2025}
}