Teaching Activities
I regularely teach the following courses:
1. Graph Theory, References: "An Introduction to Graph Theory" by D. West
and "Graph Theory" by R. Diestel
2. Algorithmic Graph Theory
3. Probabilistic Method in Graph Theory
4. Source Coding and Error Correcting Codes, References: "Elements of Information Theory"
By T. Cover, "Information and
Coding Theory" by G. A. Jones and J. M. Jones and "Coding theory" by W. J. Korner
5. Cryptography, Reference: "Cryptography: Theory and Practice" by D. Stinson
Research Areas:
Chromatic graph theory,
extremal graph theory, algorithms and complexity of graph problems,
the probabilistic methods and combinatorial structures (Latin squares and
secret sharing schemes).
The following is the list of papers classified by subjects:
Chromatic number:
1. Bounds for the b-chromatic number of some families of graphs (with Mekkia Kouider)
Discrete math. 306 (2006) 617-623 Review from MathSciNet.
2. New bounds for the chromatic number of graphs, J. Graph
Theory, June (2008) 110-122.
3. Yet another note on chromatic number and orientations, Manuscript 2008.
4. On lower bounds for the chromatic number in terms of vertex degree, Discrete Math., 311 (2011) 1365-1370.
5. On (\delta,\chi)-bounded graphs (with Andras Gyarfas), The Electronic Journal of Combinatorics 18 (2011), \#P108.
6. Bounds for chromatic number in terms of even-girth and booksize,
Discrete Math. 311 (2011) 197-204.
Grundy number and First-Fit coloring:
1.
Grundy chromatic number of the complement of bipartite graphs ,
Australas. J. Combinatorics 31 (2005) 325-329.
2. Results on the Grundy chromatic number of graphs, Discrete Math. 306 (2006) 3166-3173
Review from MathSciNet.
3. Inequalities for Grundy chromatic number of graphs,
Discrete Applied Math. 155 (2007) 2567-2572
Review from MathSciNet.
4. First-Fit coloring of graphs without an even cycle, submitted 2010.
5. The First-Fit coloring and Grundy chromatic number of graphs: A survey (In preparation).
Defining sets and greedy defining sets:
1.
Defining sets in vertex coloring of graphs and Latin rectangles (with E.S. Mahmoodian and
R. Naserasr) Discrete Math. 167 (1997) 451-460.
2.
A characterization of uniquely vertex colorable graphs using defining sets (with
H. Hajiabolhassan, M.L. Mehrabadi and R. Tuserkani) Discrete Math. 199 (1999)
233-236.
3.
Greedy defining sets of graphs ,
Australas. J. Combinatorics 23 (2001) 231-235.
4. Greedy defining sets of Latin squares, Ars Combinatoria 89 (2008) 205-222.
5.
Greedy defining sets in graphs and Latin squares ,
Electronic Notes in Discrete Math. 24 (2006) 299-302.
6. More results on greedy defining sets, accepted for publication in
Ars Combinatoria.
Spread of influence in graphs:
1. On dynamic monopolies of graphs with general thresholds, Discrete Math. accepted in 2011.
2. A study of monopolies in graphs (with K. Khoshkhah, M. Nemati, H. Soltani),
submitted 2011.
3. On dynamic monopolies of graphs: the strict and average majority thresholds,
(with K. Khoshkhah and H. Soltani), Discrete Optimization, accepted in 2012.
4. Dynamic monopolies of directed graphs (with K. Khoshkhah and H. Soltani), in preparation.
Arrays and Latin squares:
1. Maximum transversal in partial Latin squares and rainbow matchings, Discrete Applied Math.
155 (2007) 558-565.
2. Extending partial \lambda-coloring of graphs with emphasis on K_m\times K_n, Manuscript.
3. Visual cryptography of graph access structures, Manuscript.