2015/05/15 by Jeffrey H. Dinitz, Dinitz, Jeffrey H., Amelia R. W. Mattern +1 · 1 citation
Computer Science · Engineering · Mathematics · #05B30 (secondary) #05C10 (primary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Interconnection Networks and Systems #VLSI and Analog Circuit Testing #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1505.04070
openalex publication_date 2015/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2015, Archdeacon introduced the notion of Heffter arrays and showed the connection between Heffter arrays and biembedding m-cycle and an n-cycle systems on a surface. In this paper we exploit this connection and prove that for every n >= 3 there exists an orientable embedding of the complete graph on 6n+1 vertices with each edge on both a 3-cycle and an n-cycle. We also give an analogous (but partial) result for biembedding a 5-cycle system and an n-cycle system.