2023/12/31 by Michael Molloy, Molloy, Michael, Paweł Prałat +3
Biochemistry, Genetics and Molecular Biology · #Bioinformatics and Genomic Networks #Combinatorics (math.CO) #FOS: Mathematics #Gene expression and cancer classification #RNA Research and Splicing
paper · pdf · doi:10.48550/arxiv.2401.00559
openalex publication_date 2023/12/31 · openalex created_date 2024/01/03 · openalex updated_date 2026/07/28
We study the 2-offer semirandom 3-uniform hypergraph model on n vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching, and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within Θ(n) steps. Both results extend to s-uniform hypergraphs. The challenges with hypergraphs, and our methods, are qualitatively different from what has been seen for semirandom graphs. Much of our analysis is done on an auxiliary graph that is a uniform k-out subgraph of a random bipartite graph, and this tool may be useful in other contexts.