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.
On λ-fold relative Heffter arrays and biembedding multigraphs on surfaces
Costa S.;Pasotti A.
2021-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
