Amin Bahmanian

activity

20172026

most citedMultiply Balanced Edge Colorings of Multigraphs

25 citations · 65 across the 20 of their papers we have counts for

collaborators

23 papers

math.CO2026

Connected Fair Detachments of Hypergraphs II

Amin Bahmanian

We study embeddings of factorizations of the $λ$ -fold complete $h$ -uniform hypergraph $λ K_{m}^{h}$ in factorizations of $λ K_{n}^{h}$ , where $m < n$ and both the source and target degrees may…

math.CO2026

A Hadamard Cube of Order 22

Amin Bahmanian, Sho Suda

We give an explicit three-dimensional Hadamard matrix of order $22$ . The example is presented by listing its twenty-two $22 \times 22$ two-dimensional slices.

math.CO2026

Sudoku Analogues of Baranyai's Theorem

Amin Bahmanian, Sho Suda

Motivated by higher-dimensional generalizations of Sudoku, we study exact block-structured decompositions, algebraic characterizations, and orthogonality for Sudoku hypercubes. Let…

math.CO2026

Extending Symmetric Layer-Rainbow Latin Cubes

Amin Bahmanian

An $n \times n \times n$ array on $n^{2}$ symbols is a layer-rainbow Latin cube if every layer contains every symbol exactly once. We call it symmetric if $L_{ij\ell}=L_{j\ell i}=L_{\e…

math.CO2026

The Andersen-Hoffman Theorem for Equitable Rectangles

Amin Bahmanian, Anna Johnsen-Yu

More than forty years ago, Andersen and Hoffman independently proved that every symmetric Latin rectangle can be extended to a symmetric Latin square with prescribed diagonal entri…

math.CO2026

Embedding Equitable Rectangles

Amin Bahmanian, Anna Johnsen-Yu

Completing partial Latin squares is NP-complete. Ryser characterized precisely when an $r \times s$ Latin rectangle can be completed to an $n \times n$ Latin square. We extend this t…

math.CO2026

Hadamard Hypercubes

Amin Bahmanian, Sho Suda

Although Hadamard matrices have been investigated since the nineteenth century, relatively little is known about their higher-dimensional analogues. In this paper, we introduce two…

math.CO2025

Ryser's Theorem for Simple Multi-Latin Rectangle

Amin Bahmanian

We prove a general result on completing objects similar to Latin rectangles in which the number of occurrences of each symbol is prescribed, each cell contains multiple symbols, an…

math.CO2024

Spanning Euler Tours in Hypergraphs

Amin Bahmanian, Songling Shan

Motivated by generalizations of de Bruijn cycles to various combinatorial structures (Chung, Diaconis, and Graham), we study various Euler tours in set systems. Let $G$ b…

math.CO2022

Embedding Irregular Colorings into Connected Factorizations

Amin Bahmanian, Anna Johnsen

For $r := (r_{1}, \dots, r_{k})$ , an $r$ -factorization of the complete $λ$ -fold $h$ -uniform $n$ -vertex hypergraph $λ K_{n}^{h}$ is a partition of (the edges of) $λ K_{n}^{h}$ into $F_{1}, \dots, F_{k}$ s…

math.CO2022★ 1 cited

Toward a Three-dimensional Counterpart of Cruse's Theorem

Amin Bahmanian

Completing partial latin squares is NP-complete. Motivated by Ryser's theorem for latin rectangles, in 1974, Cruse found conditions that ensure a partial symmetric latin square of…

math.CO2022

Sharp Embeddings of Layer-Rainbow Cubes and Orthogonal Pairs

Amin Bahmanian

We determine the exact extension threshold for one-factorizations of complete tripartite $3$ -uniform hypergraphs. Equivalently, for $n > m$ , every order- $m$ layer-rainbow cube embeds…

math.CO2022

Ryser's Theorem for Symmetric $ρ$ -latin Squares

Amin Bahmanian, A. J. W. Hilton

Let $L$ be an $n \times n$ array whose top left $r \times r$ subarray is filled with $k$ different symbols, each occurring at most once in each row and at most once in each column. W…

math.CO2022

Symmetric Layer-Rainbow Colorations of Cubes

Amin Bahmanian

Can we color the $n^{3}$ cells of an $n \times n \times n$ cube $L$ with $n^{2}$ colors in such a way that each layer parallel to each face contains each color exactly once and that the…

math.CO2022

On Factors with Prescribed Degrees in Bipartite Graphs

Amin Bahmanian

We establish a new criterion for a bigraph to have a subgraph with prescribed degree conditions. We show that the bigraph $G [X, Y]$ has a spanning subgraph $F$ such that $g(x)\leq d…

math.CO2022★ 1 cited

Ryser's Theorem for $ρ$ -latin Rectangles

Amin Bahmanian

Let $L$ be an $n \times n$ array whose top left $r \times s$ subarray is filled with $k$ different symbols, each occurring at most once in each row and at most once in each column. W…

math.CO2020★ 1 cited

Connected Fair Detachments of Hypergraphs I

Amin Bahmanian

Let $G$ be a hypergraph whose edges are colored. An {\it $(α, n)$ -detachment} of $G$ is a hypergraph obtained by splitting a vertex $α$ into $n$ vertices, say $α_1…

math.CO2018

Resolvable Cycle Decompositions of Complete Multigraphs and Complete Equipartite Multigraphs via Layering and Detachment

Amin Bahmanian, Mateja Šajna

We construct new resolvable decompositions of complete multigraphs and complete equipartite multigraphs into cycles of variable lengths (and a perfect matching if the vertex degree…

math.CO2018★ 2 cited

Partitioning The Edge Set of a Hypergraph Into Almost Regular Cycles

Amin Bahmanian, Sadegheh Haghshenas

A cycle of length $t$ in a hypergraph is an alternating sequence $v_{1}, e_{1}, v_{2} \dots, v_{t}, e_{t}$ of distinct vertices $v_{i}$ and distinct edges $e_{i}$ so that $\{v_i,v_{i+1}\}\subseteq e_…

math.CO2017★ 10 cited

Embedding factorizations for 3-uniform hypergraphs

Amin Bahmanian, Chris Rodger

In this paper, two results are obtained on a hypergraph embedding problem. The proof technique is itself of interest, being the first time amalgamations have been used to address t…

math.CO2017★ 4 cited

Embedding an Edge-colored $K (a^{(p)}; λ, μ)$ into a Hamiltonian Decomposition of $K (a^{(p + r)}; λ, μ)$

Amin Bahmanian, Chris Rodger

Let $K (a^{(p)}; λ, μ)$ be a graph with $p$ parts, each part having size $a$ , in which the multiplicity of each pair of vertices in the same part (in different parts) is $λ$ ( $μ$ , res…

math.CO2017★ 21 cited

Detachments of Hypergraphs I: The Berge-Johnson Problem

Amin Bahmanian

A detachment of a hypergraph is formed by splitting each vertex into one or more subvertices, and sharing the incident edges arbitrarily among the subvertices. For a given edge-col…

math.CO2017★ 25 cited

Multiply Balanced Edge Colorings of Multigraphs

Amin Bahmanian, Chris Rodger

In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so…

Connected Fair Detachments of Hypergraphs II

A Hadamard Cube of Order 22

Sudoku Analogues of Baranyai's Theorem

Extending Symmetric Layer-Rainbow Latin Cubes

The Andersen-Hoffman Theorem for Equitable Rectangles

Embedding Equitable Rectangles

Hadamard Hypercubes

Ryser's Theorem for Simple Multi-Latin Rectangle

Spanning Euler Tours in Hypergraphs

Embedding Irregular Colorings into Connected Factorizations

Toward a Three-dimensional Counterpart of Cruse's Theorem

Sharp Embeddings of Layer-Rainbow Cubes and Orthogonal Pairs

Ryser's Theorem for Symmetric ρ-latin Squares

Symmetric Layer-Rainbow Colorations of Cubes

On Factors with Prescribed Degrees in Bipartite Graphs

Ryser's Theorem for ρ-latin Rectangles

Connected Fair Detachments of Hypergraphs I

Resolvable Cycle Decompositions of Complete Multigraphs and Complete Equipartite Multigraphs via Layering and Detachment

Partitioning The Edge Set of a Hypergraph Into Almost Regular Cycles

Embedding factorizations for 3-uniform hypergraphs

Embedding an Edge-colored K(a(p);λ,μ) into a Hamiltonian Decomposition of K(a(p+r);λ,μ)

Detachments of Hypergraphs I: The Berge-Johnson Problem

Multiply Balanced Edge Colorings of Multigraphs

Ryser's Theorem for Symmetric $ρ$ -latin Squares

Ryser's Theorem for $ρ$ -latin Rectangles

Embedding an Edge-colored $K (a^{(p)}; λ, μ)$ into a Hamiltonian Decomposition of $K (a^{(p + r)}; λ, μ)$