On the spectrum of the forced matching number of graphs (2009)
Afshani, Peyman, Hatami, Hamed, Mahmoodian, Ebadollah S.
Let $G$ be a graph that admits a perfect matching. A {\sf forcing set} for a perfect matching $M$ of $G$ is a subset $S$ of $M$, such that $S$ is contained in no other perfect matching of $G$. This...
Circular Chromatic Index of Graphs of Maximum Degree 3 (2007)
Peyman Afshani Mahsa, Peyman Afshani, Mahsa Ghandehari, Mahya Ghandehari, Hamed Hatami, Ruzbeh Tusserkani, ...
This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then c (G) 11=3 provided that G does not contain H1 or H2 as a subgraph, where H1 and H2 are obtained by...
On approximate range counting and depth (2007)
ABSTRACT We improve the previous results by Aronov and Har-Peled (SODA'05) and Kaplan and Sharir (SODA'06) and present a randomized data structure of O(n) expected size which can answer 3D...
Afshani, Peyman, Hatami, Hamed
We prove algorithmic and hardness results for the problem of finding the largest set of a fixed diameter in the Euclidean space. In particular, we prove that if $A^*$ is the largest subset of...
Circular chromatic index of graphs of maximum degree 3 (2006)
Afshani, Peyman, Ghandehari, Mahsa, Ghandehari, Mahya, Hatami, Hamed, Tusserkani, Ruzbeh, Zhu, Xuding
This paper proves that if $G$ is a graph (parallel edges allowed) of maximum degree 3, then $\chi_c'(G) \leq 11/3$ provided that $G$ does not contain $H_1$ or $H_2$ as a subgraph, where $H_1$ and...
Dynamic connectivity for axis-parallel rectangles (2006)
Peyman Afshani, Timothy M. Chan
Abstract. In this paper we give a fully dynamic data structure to maintain the connectivity of the intersection graph of n axis-parallel rectangles. The amortized update time (insertion and deletion...