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]