India is a country with a deep and vast mathematical and scientific heritage right since the Vedic times (ca. 5000 BC) and volumes have been written about this.  The oldest known mathematical work is the “Sulba-Sutras” jointly composed around 800 BC by Baudhayana, Apastamba and Katyayana.  In the Sulba-sutras we see an explicit statement of the Pythagoras theorem and its various applications in geometric constructions.

    Among the various concepts of mathematics that originated and were developed in India, a few prominent ones are – the number ‘zero’ and the decimal system, fundamental arithmetic operations, solution of equations in integers, introduction of negative numbers, most of the standard formulas involving sine and cosine functions and power series representation of trigonometric functions.  These were due to the works of Pingala (200 BC), Aryabhata (499 AD), Brahmagupta (628 AD), Sridharacharya (750 AD) and many others.

    A special mention has to be made about calculus in India.  It was believed that Indian mathematics remained barren during the period from 13th century to the 18th century.  But, historians of mathematics can now convince the entire world that in Kerala there was a rich tradition of mathematics during that period. Madhavan(ca. 1340 – 1425) who lived in Kerala broke the finite barrier and contributed to the concept of infinite series expansions.  In fact he deserves to be called the father of infinitesimal analysis.  Parameswaran, Nilakantan, Jyeshtadevan, Sankara Variyar, and many others who lived in Kerala during this period contributed significantly to various branches of mathematics. At this juncture, it is to be specially mentioned that ‘Lilavati’ the magnum opus of Bhaskara II, has been translated into Malayalam (the language of Kerala) and was first published in 2008.

    India has also had a rich tradition of combinatorial thought since the time of Pingala. In his Chandas – Sutra he considers the method of finding the number of combinations obtainable by taking one, two or more letters out of a given number of letters.  He mentions a term, ‘Meru Prastara’ which is exactly the same as the modern Pascal’s triangle. Mahavira (650 A.D.) also made some contributions to the theory of combinations in his magnum opus ‘Ganithasara Samgraha’. N.L. Biggs, E.K. Lloyd and R.J.Wilson have remarked, “It is strange that there is almost no material relevant to Combinatorics in the literature of the classical western civilization.  All the evidence points to the fact that the originators of the subject came from the East.  The main stimulus came from the Hindus”.  It is also known that the modern concepts of permutations and combinations  – formulas for the number of permutations of an n-set and the number of k-subsets of an n-set, date back to Bhaskara (1114 – 1185)  and  Brahmagupta respectively. 

    The contributions of the legendary mathematical monk, S.Ramanujan continues to influence almost all areas of mathematics.  The disproof  of the famous conjecture (1782) of Leonhard Euler on the ‘mutually orthogonal Latin squares’ by Indian mathematicians R.C. Bose, S.S. Shrikhande, and E. T. Parker in 1959 was a major breakthrough.  This ushered in the study of ‘Combinatorial Designs’ in India.

    The logo of this conference is the ‘Shrikhande Graph’.

    The Government of India through its various ministries, is supporting in a big way, the research in discrete mathematics. We have very active research groups in many esteemed academic institutions such  as the  Tata Institute of Fundamental Research, The Institute of Mathematical Sciences (Chennai), Indian Institute of Science(Bangalore), Indian Statistical Institutes, Indian Institutes of Technology, University of Mumbai(Mumbai), M.S.University (Tirunelveli), Annamalai University (Annamalai Nagar), Kalasalingam University (Krishnankoil), Bharathidasan University (Trichy), Anna University (Chennai), University of Mysore (Mysore), University of Kerala (Trivandrum), and Cochin University of Science and Technology – the host university of ICRTGC, to mention a few.

    The aim of this conference is to bring together all those working in different areas of combinatorics and graph theory, be theoretical or algorithmic, from different parts of the world and to provide a fruitful forum for collaborative research.

    The treasure of beauty and charm that nature has lavished on Kerala’s landscape thrills the aesthetic sense of any visitor and makes him exclaim that this  really is a ‘paradise on earth’. Kerala which literally means the ‘land of coconuts’ is also the birth place of the internationally acclaimed art form – Kathakali.

    We are sure that all of you will experience firsthand the essence of Indian culture encapsuled in the Sanskrit phrase ‘Athithi Devo Bhava’ which means ‘Guests are God’.

    We look forward to an international academic get together of enviable standards.

    On behalf of the organizing committee of ICRTGC, I welcome you all to Kerala – God’s Own Country and the magnificent city of Cochin (Ernakulam) – The Queen of the Arabian sea.

Ambat Vijayakumar
Convener,   ICRTGC-2010

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