5 citations · 8 across the 15 of their papers we have counts for
15 papers · 1 filter
The mapping index through the lens of the cross-index
Vuong Bui, Hamid Reza Daneshpajouh, Roman Karasev
We study the cross-index of free \(G\)-posets as a combinatorial analogue of the equivariant topological index. We demonstrate that the cross-index exhibits many structural propert…
On the Chromatic Number of Stable Kneser Hypergraphs: Verifying the Conjecture for New Families
Hamid Reza Daneshpajouh
One of the key unsolved conjectures in hypergraph coloring is about the chromatic number of -stable -uniform Kneser hypergraphs . The pr…
Box complexes: at the crossroad of graph theory and topology
Hamid Reza Daneshpajouh, Frédéric Meunier
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bou…
A topological version of Hedetniemi's conjecture for equivariant spaces
Vuong Bui, Hamid Reza Daneshpajouh
A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two -spaces is equal to the minimum of their $\mathbb Z/2…
A counterexample to a conjecture on the chromatic number of r-stable Kneser hypergraphs
Hamid Reza Daneshpajouh
The main purpose of this note is to give a counterexample to the following conjecture, raised by Florian Frick [\textit{Int. Math. Res. Not. IMRN 2020 (13), 4037-4061 (2020)}]. Con…
On the number of star-shaped classes in optimal colorings of Kneser graphs
Hamid Reza Daneshpajouh
A family of sets is called star-shaped if all the members of the family have a point in common. The main aim of this paper is to provide a negative answer to the following question…
Colorings of complements of line graphs
Hamid Reza Daneshpajouh, Frédéric Meunier, Guilhem Mizrahi
Our purpose is to show that complements of line graphs enjoy nice coloring properties. We show that for all graphs in this class the local and usual chromatic numbers are equal. We…
On the neighborhood complex of -stable Kneser graphs
Hamid Reza Daneshpajouh, József Osztényi
In 2002, A. Björner and M. de Longueville showed the neighborhood complex of the -stable Kneser graph has the same homotopy type as the -s…
Hedetniemi's conjecture from the topological viewpoint
Hamid Reza Daneshpajouh, Roman Karasev, Alexey Yu. Volovikov
This paper is devoted to studying a topological version of the famous Hedetniemi conjecture which says: The -index of the Cartesian product of two -spaces…
On the chromatic number of generalized Kneser hypergraphs
Hamid Reza Daneshpajouh
The generalized Kneser hypergraph is the hypergraph whose vertices are all the -subsets of , and edges are -tuples of distinct vertices such…
Dold's Theorem from Viewpoint of Strong Compatibility Graphs
Hamid Reza Daneshpajouh
Let be a non-trivial finite group. The well-known Dold's theorem states that: There is no continuous -equivariant map from an -connected simplicial -complex to a free…
Chromatic number, Clique number, and Lovász's bound: In a comparison
Hamid Reza Daneshpajouh
In the way of proving Kneser's conjecture, László Lovász settled out a new lower bound for the chromatic number. He showed that if neighborhood complex of a graph…
On Björner and Lovász's conjecture
Hamid Reza Daneshpajouh
In the way of proving Kneser's conjecture, László Lovász settled out a new lower bound for the chromatic number of graphs. He showed that if the hom complex $||Hom(\mathcal{K}_2, H…
New construction of graphs with high chromatic number and small clique
Hamid Reza Daneshpajouh
In this note, we introduce a new method for constructing graphs with high chromatic number and small clique. Indeed, via this method, we present a new proof for the well-known Knes…
A topological lower bound for the chromatic number of a special family of graphs
Hamid Reza Daneshpajouh
For studying topological obstructions to graph colorings, Hom-complexes were introduced by Lovász. A graph is called a test graph if for every graph , the -connectedness…