Matchings in Random Biregular Bipartite Graphs

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and Renyi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Comment: 30 pages and 3 figures - Latest version has updated introduction and bibliograph

Matchings in random biregular bipartite graphs

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Peer ReviewedPostprint (published version

Global eigenvalue fluctuations of random biregular bipartite graphs

We compute the eigenvalue fluctuations of uniformly distributed random biregular bipartite graphs with fixed and growing degrees for a large class of analytic functions. As a key step in the proof, we obtain a total variation distance bound for the Poisson approximation of the number of cycles and cyclically non-backtracking walks in random biregular bipartite graphs, which might be of independent interest. As an application, we translate the results to adjacency matrices of uniformly distributed random regular hypergraphs.Comment: 45 pages, 5 figure

TEMPORAL CONNECTIVITY AS A MEASURE OF ROBUSTNESS IN NONORTHOGONAL MULTIPLE ACCESS WIRELESS NETWORKS

Supplementary Material has been provided, but is not yet published.Nonorthogonal multiple access (NOMA) is recognized as an important technology to meet the performance requirements of fifth generation (5G) and beyond 5G (B5G) wireless networks. Through the technique of overloading, NOMA has the potential to support higher connection densities, increased spectral efficiency, and lower latency than orthogonal multiple access. The role of NOMA in 5G/B5G wireless networks necessitates a clear understanding of how overloading variability affects network robustness. This dissertation considers the relationship between variable overloading and network robustness through the lens of temporal network theory, where robustness is measured through the evolution of temporal connectivity between network devices (ND). We develop a NOMA temporal graph model and stochastic temporal component framework to characterize time-varying network connectivity as a function of NOMA overloading. The analysis is extended to derive stochastic expressions and probability mass functions for unidirectional connectivity, bidirectional connectivity, the inter-event time between unidirectional connectivity, and the minimum time required for bidirectional connectivity between all NDs. We test the accuracy of our analytical results through numerical simulations. Our results provide an overloading-based characterization of time-varying network robustness that is generalizable to any underlying NOMA implementation.National Security Agency, Fort George G. Meade, MD 20775Major, United States Marine CorpsApproved for public release. Distribution is unlimited

Matchings in random biregular bipartite graphs

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Peer Reviewe

Matchings in random biregular bipartite graphs

We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdös and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.Peer Reviewe