“Ebadollah S. Mahmoodian”

Tel:  (+98)(21)22290928
Fax:  (+98)(21)22290648

IPM Positions

Senior Associate Researcher, School of Mathematics
(2007 - 2008
(Until June))

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics
(2001 - 2002)
Associate Researcher (non-resident), School of Mathematics
(1994 - 1996)

Non IPM Affiliations

Professor of Sharif University of Technology

Research Activities

Let G be a graph that admits a perfect matching. A 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 concept is studied in different areas of combinatorics under the name of defining sets or critical sets. For example a critical set in an n ×n array is a set C of given entries, such that there exists a unique extension of C to an n×n Latin square and no proper subset of C has this property.

Last year in our project with IPM , we studied the problem of the spectra of the sizes of these sets. These results motivated us greatly and revealed the connection of this subject to the other problems such as the critical sets in Latin squares, specially the largest sizes of such sets.

In the present project we will study this connection in detail.

Present Research Project at IPM

Defining sets in perfect matchings and Latin squares

Related Papers

1. E. S. Mahmoodian (Joint with A. A. Khanban and M. Mahdian)
A linear algebraic approach to orthogonal arrays and latin squares
Ars Combin. (Accepted) [abstract]
2. P. Afshani, H. Hatami and E. S. Mahmoodian
On the spectrum of the forced matching number of graphs
Australas. J. Combin. 30 (2004), 147-160  [abstract]
3. H. Hatami and E. S. Mahmoodian
A lower bound for the size of the largest critical sets in Latin squares
Bull. Inst. Combin. Appl. 38 (2003), 19-22  [abstract]
4. D. Donovan and E. S. Mahmoodian
An algorithm for writing any Latin interchange as a sum of intercalates
Bull. Inst. Combin. Appl. 34 (2002), 90-98  [abstract]
5. E. S. Mahmoodian and N. Soltankhah
A linear algebraic approach to directed designs
Australas. J. Combin. 23 (2001), 119-134  [abstract]
6. M. Ghebleh and E. S. Mahmoodian
On uniquely list colorable graphs
Ars Combin. 59 (2001), 307-318  [abstract]
7. E. S. Mahmoodian, N. Soltankhah and A. Penfold Street
On defining sets of directed designs
Australas. J. Combin. 19 (1999), 179-190  [abstract]
8. E. S. Mahmoodian and E. Mendelsohn
On defining numbers of vertex colouring of regular graphs
Discrete Math. 197/198 (1999), 543-554  [abstract]
9. E. S. Mahmoodian
Defining sets and uniqueness in graph colorings: A survey
J. Statist. Plann. Inference 73 (1998), 85-89  [abstract]
10. S. Akbari, M. Behzad, H. Hajiabolhassan and E. S. Mahmoodian
Uniquely total colorable graphs
Graphs Combin. 13 (1997), 305-314  [abstract]
11. E. S. Mahmoodian and G.H.J. Van Rees
Critical sets in back circulant latin rectangles
Australas. J. Combin. 16 (1997), 45-50  [abstract]
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