Relative Heffter arrays and biembeddings

DOI10.26493/1855-3974.2110.6f2zbMath1464.05030arXiv1909.03064OpenAlexW3034195266MaRDI QIDQ4988851

Simone Costa, Marco Antonio Pellegrini, Anita Pasotti

Publication date: 19 May 2021

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.03064

zbMATH Keywords

biembeddingHeffter arraymultipartite complete graph

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Planar graphs; geometric and topological aspects of graph theory (05C10) Other designs, configurations (05B30) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (12)

Non-zero sum Heffter arrays and their applications ⋮ Magic rectangles, signed magic arrays and integer $\lambda$-fold relative Heffter arrays ⋮ Rectangular Heffter arrays: a reduction theorem ⋮ Magic partially filled arrays on abelian groups ⋮ Weak Heffter arrays and biembedding graphs on non-orientable surfaces ⋮ On the existence of integer relative Heffter arrays ⋮ A generalization of Heffter arrays ⋮ Tight globally simple nonzero sum Heffter arrays and biembeddings ⋮ Orthogonal cycle systems with cycle length less than 10 ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On \(\lambda\)-fold relative Heffter arrays and biembedding multigraphs on surfaces

Cites Work

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• Heffter arrays and biembedding graphs on surfaces
• On Partial Sums in Cyclic Groups
• On perfect Γ-decompositions of the complete graph
• Combinatorial Local Planarity and the Width of Graph Embeddings
• Biembedding Steiner Triple Systems and n-cycle Systems on Orientable Surfaces
• The existence of square integer Heffter arrays
• Globally simple Heffter arrays and orthogonal cyclic cycle decompositions
• A tour problem on a toroidal board
• On strongly sequenceable abelian groups
• The existence of square non-integer Heffter arrays
• Distinct partial sums in cyclic groups: polynomial method and constructive approaches
• Tight Heffter Arrays Exist for all Possible Values
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