2023/06/13 by Louis Golowich, Golowich, Louis · 3 citations
Mathematics · #05C48 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2306.07551
openalex publication_date 2023/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We present a new explicit construction of onesided bipartite lossless expanders of constant degree, with arbitrary constant ratio between the sizes of the two vertex sets. Our construction is simpler to state and analyze than the only prior construction of Capalbo, Reingold, Vadhan, and Wigderson (2002), and achieves improvements in some parameters. We construct our lossless expanders by imposing the structure of a constant-sized lossless expander "gadget" within the neighborhoods of a large bipartite spectral expander; similar constructions were previously used to obtain the weaker notion of unique-neighbor expansion. Our analysis simply consists of elementary counting arguments and an application of the expander mixing lemma.