7 papers
Bipartite Turán Numbers of Trees and Star Forests
Omid Khormali
The bipartite Turán number of a graph , denoted , is the maximum number of edges in any -free bipartite graph with parts of size $|A| = m…
Gap-Sums via Quasi-Arithmetic Means with Applications to Fibonacci and Lucas Sequences
Omid Khormali, Ghaya Mtimet, Nuh Aydin +1
We develop a unified framework for studying the integers missing between consecutive terms of an increasing integer sequence, extending Barry's arithmetic gap-sum to geometric and…
On the History of the Square and Multiply Algorithm
Nuh Aydin, Mohammad K. Azarian, Omid Khormali +1
The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a standard method for fast exponentiation in modern computation. Its historical orig…
From Historical Puzzles to Grammatical Constraints: Circular Partitions, Generalized Run-Length Encodings, and Polynomial-Time Decidability
Omid Khormali, Ghaya Mtimet, Nuh Aydin
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic…
On Link-irregular Digraphs
Alexander Bastien, Omid Khormali
We extend the study of link-irregular graphs to directed graphs (digraphs), where a digraph is link-irregular if no two vertices have isomorphic directed links. We establish that l…
On Link-irregular labelings of Graphs
Alexander Bastien, Omid Khormali
We introduce the concept of link-irregular labelings for graphs, extending the notion of link-irregular graphs through edge labeling with positive integers. A labeling is link-irre…