On λ-fold relative Heffter arrays and biembedding multigraphs on surfaces. (October 2021)

• Record Type: Journal Article
• Authors: Costa, Simone; Pasotti, Anita
• Is Part Of: European journal of combinatorics. Volume 97(2021)
• Publication Date: 2021-10
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2021.103370
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: In this paper we define a new class of partially filled arrays, called λ -fold relative Heffter arrays, that are a generalization of the Heffter arrays introduced by Archdeacon in 2015. After showing the connection of this new concept with several other ones, such as signed magic arrays, graph decompositions and relative difference families, we determine some necessary conditions and we present existence results for infinite classes of these arrays. In the last part of the paper we also show that these arrays give rise to biembeddings of multigraphs into orientable surfaces and we provide infinite families of such biembeddings. To conclude, we present a result concerning pairs of λ -fold relative Heffter arrays and covering surfaces.