Matchings in Random Biregular Bipartite Graphs
Guillem Perarnau, Giorgis Petridis
TL;DR
This paper investigates the existence of perfect matchings in random biregular bipartite graphs, extending classical results and applying findings to commutative graphs in additive number theory.
Contribution
It proves a new theorem on perfect matchings in random biregular bipartite graphs and connects these results to applications in additive number theory.
Findings
Established conditions for perfect matchings in random biregular bipartite graphs.
Extended Erdős-Rényi theorem to a biregular bipartite setting.
Applied results to the study of commutative graphs in additive number theory.
Abstract
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.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications