A survey of Heffter arrays

DOI10.1007/978-3-031-48679-1_20zbMATH Open1548.05067MaRDI QIDQ6613375

J. H. Dinitz, Anita Pasotti

Publication date: 2 October 2024

zbMATH Keywords

biembeddingcycle systemHeffter array

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Other designs, configurations (05B30)

Cites Work

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• Cyclic biembeddings of twofold triple systems
• Existence of some signed magic arrays
• Sequences in groups with distinct partial products
• Square integer Heffter arrays with empty cells
• Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs
• A non-existence result on cyclic cycle-decompositions of the cocktail party graph
• Skolem-type difference sets for cycle systems
• A problem on partial sums in abelian groups
• Existence of cyclic \(k\)-cycle systems of the complete graph
• Resolvable configurations
• On \(\lambda\)-fold relative Heffter arrays and biembedding multigraphs on surfaces
• Non-zero sum Heffter arrays and their applications
• On sequences in cyclic groups with distinct partial sums
• On the existence of integer relative Heffter arrays
• Some new results about a conjecture by Brian Alspach
• Globally simple heffter arrays \(H ( n ; k )\) when \(k \equiv 0 , 3 \pmod 4 \)
• Heffter arrays and biembedding graphs on surfaces
• Cyclic Hamiltonian cycle systems of the complete graph minus a 1-factor
• Directed paths of diagonals within polygons
• Sequenceable groups and related topics.
• Rectangular Heffter arrays: a reduction theorem
• Graphs on surfaces
• Further biembeddings of twofold triple systems
• On Partial Sums in Cyclic Groups
• Cyclicm-cycle systems withm ≤ 32 orm = 2q withq a prime power
• Signed magic rectangles with three filled cells in each column
• Combinatorial Local Planarity and the Width of Graph Embeddings
• Combinatorial Nullstellensatz
• Cyclic $m$-cycle systems of complete graphs minus a 1-factor
• 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
• Cyclick-cycle systems of order 2kn +k: A solution of the last open cases
• Relative Heffter arrays and biembeddings
• New results on modular Golomb rulers, optical orthogonal codes and related structures
• Magic rectangles, signed magic arrays and integer $\lambda$-fold relative Heffter arrays
• Magic rectangles with empty cells
• 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
• Mutually orthogonal cycle systems
• Magic partially filled arrays on abelian groups
• Weak Heffter arrays and biembedding graphs on non-orientable surfaces
• A generalization of Heffter arrays
• Tight globally simple nonzero sum Heffter arrays and biembeddings
• Weak sequenceability in cyclic groups
• Biembeddings of cycle systems using integer Heffter arrays
• Tight Heffter arrays from finite fields
• On the number of non-isomorphic (simple) \(k\)-gonal biembeddings of complete multipartite graphs

Related Items (4)

Tight Heffter arrays from finite fields ⋮ Heffter spaces ⋮ On the number of non-isomorphic (simple) \(k\)-gonal biembeddings of complete multipartite graphs ⋮ Additivity of symmetric and subspace 2-designs

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