B. Miraftab

The Volume Helly Theorem in the plane, colorful version

Imre Bárány, Bobby Miraftab, Leonidas Theocharous

We prove a colorful volume Helly theorem for convex sets in $R^{2}$ : There is a constant $V > 0$ such that if $F_{1}, F_{2}, F_{3}, F_{4}$ are fini…

On $ε$ -Matrix Product Factorization of graphs

Farzad Maghsoudi, Bobby Miraftab, Sho Suda

We introduce an approximate version of matrix product factorization for graphs. A simple graph $G$ on $n$ vertices is said to admit an $ε$ -matrix product factorization if…

Automorphism Groups in Extremal Families of Polyhedral Graphs

Riccardo W. Maffucci, Bobby Miraftab

We study automorphism groups in five extremal families of polyhedral graphs. For every $n \geq 14$ , we prove that every minimum-order $3$ -polytopal graph containing a vertex of each d…

On Matrix Product Factorization in Association Schemes

Allen W. Herman, Bobby Miraftab

We study matrix product factorizations (MPFs) in symmetric association schemes: identities $A_{S} A_{T} = A_{U}$ where $A_{S}, A_{T}, A_{U}$ are loopless unions of basic relations and the ordinary…

Cayley Graphs Of Order $pq r s$ Are Hamiltonian

Florian Lehner, Farzad Maghsoudi, Bobby Miraftab

Assume $G$ is a finite group with order $∣ G ∣ = pq r s$ , where $p$ , $q$ , $r$ , and $s$ are distinct prime numbers. We prove that every connected Cayley graph of $G$ conta…

Separation profiles of hyperbolic planar and apex-minor-free graphs

Joseph P. MacManus, Bobby Miraftab

We show that the separation profile of a hyperbolic planar graph and, more generally, a hyperbolic apex-minor-free graph, grows at most logarithmically, answering a question of Ben…

Vertex cuts and median decompositions

Joseph P. MacManus, Bobby Miraftab

Median decompositions were introduced by Stavropoulos in 2015 as a generalisation of tree decompositions. In this paper, we further develop and exposit this theory as a tool in str…

On the Spectra of Digraph Laplacians

Saieed Akbari, Michael Cavers, Farzad Maghsoudi +1

We present several Laplacian-type matrices associated with a loopless digraph $D$ : the out-/in-degree Laplacians $L_{out}, L_{in}$ , the incidence…

Spectra of Subdivision Products of Digraphs

Michael Cavers, Farzad Maghsoudi, Babak Miraftab

This paper introduces four types of subdivision products for simple directed graphs extending those from the undirected case, in particular, the subdivision-vertex join, subdivisio…

2-dimensional unit vector flows

Hussein Houdrouge, Bobby Miraftab, Pat Morin

We study $2$ -dimensional unit vector flows on graphs, that is, nowhere-zero flows that assign to each oriented edge a unit vector in $R^{3}$ . We give a new geometric charac…

Basis Number and Pathwidth

Babak Miraftab, Pat Morin, Yelena Yuditsky

We prove two results relating the basis number of a graph $G$ to path decompositions of $G$ . Our first result shows that the basis number of a graph is at most four times its pathw…

On Prime Matrix Product Factorizations

Saieed Akbari, Mohamad Parsa Elahimanes, Bobby Miraftab

A graph $G$ factors into graphs $H$ and $K$ via a matrix product if $A = B C$ , where $A$ , $B$ , and $C$ are the adjacency matrices of $G$ , $H$ , and $K$ , respectively. The graph $G$ i…

On Matrix Product Factorization of Cayley graphs

Allen W. Herman, Bobby Miraftab

We study when the adjacency matrix of a Cayley graph factors as the product of two adjacency matrices of Cayley graphs. Let $G$ be a finite group and let $U\subseteq G\setminus \{e…

Spectra of Corona Products of Digraphs

Michael Cavers, Farzad Maghsoudi, Babak Miraftab

Two types of corona products for simple directed graphs are introduced, extending the classical notions from the undirected setting: the vertex-corona and the arc-corona. Their str…

Separation Number and Treewidth, Revisited

Hussein Houdrouge, Babak Miraftab, Pat Morin

We give a constructive proof of the fact that the treewidth of a graph $G$ is bounded by a linear function of the separation number of $G$ .

The basis number of 1-planar graphs

Saman Bazargani, Therese Biedl, Prosenjit Bose +2

Let $B$ be a set of Eulerian subgraphs of a graph $G$ . We say $B$ forms a $k$ -basis if it is a minimum set that generates the cycle space of $G$ , and any edge of $G$ lies in at mos…

Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $Z_{p}$ as Commutator Subgroups

Florian Lehner, Farzad Maghsoudi, Babak Miraftab

In 1982, Durnberger proved that every connected Cayley graph of a finite group with a commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend this…

On the $d$ -independence number in 1-planar graphs

Therese Biedl, Prosenjit Bose, Babak Miraftab

The $d$ -independence number of a graph $G$ is the largest possible size of an independent set $I$ in $G$ where each vertex of $I$ has degree at least $d$ in $G$ . Upper bounds for t…

math.CO2024★ 1 cited

Basis number of bounded genus graphs

Florian Lehner, Babak Miraftab

The basis number of a graph $G$ is the smallest integer $k$ such that $G$ admits a basis $B$ for its cycle space, where each edge of $G$ belongs to at most $k$ members of $B$ . In t…

Sparse graphs with local covering conditions on edges

Debsoumya Chakraborti, Amirali Madani, Anil Maheshwari +1

In 1988, Erdős suggested the question of minimizing the number of edges in a connected $n$ -vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman…

Spectral Methods for Matrix Product Factorization

Saieed Akbari, Yi-Zheng Fan, Fu-Tao Hu +2

A graph $G$ is factored into graphs $H$ and $K$ via a matrix product if there exist adjacency matrices $A$ , $B$ , and $C$ of $G$ , $H$ , and $K$ , respectively, such that $A = B C$ . In…