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Mehdi Behzad
Mehdi Behzad (Persian:مهدی بهزاد) (born April 22, 1936) is a prominent mathematician of Iranian origin specializing in graph theory. He introduced his Total coloring theory (widely known as Behzad's Conjecture or the Total Chromatic Number Conjecture) in 1965 as part of his Ph.D. dissertation.〔(M. Behzad, ''Graphs and Their Chromatic Numbers'', Michigan State University, Department of Mathematics, 1965, 124 pages. )〕 In spite of active work, including publication of books and hundreds of papers, as well as partial results in the last 50 years,〔(H. P. Yap, ''Total Colouring of Graphs'', Springer, 2009, 131 pages. )〕 this conjecture remains as challenging as it is open. In fact, Behzad's Conjecture now belongs to mathematics’ classic open problems.〔(Alexander Soifer, ''The Mathematical Coloring Book'', Springer, 2009, 607 pages. )〕
==Graph Theory==
Behzad is the coauthor of two text books on graph theory published in 1972 and 1979 in the United States,〔(M. Behzad and G. Chartrand, ''Introduction to the Theory of Graphs'', Allyn and Bacon, 1971, 271 pages. )〕〔(M. Behzad, G. Chartrand, and L. Lesniak, ''Graphs & Digraphs'', Wadsworth, Inc., 1979, 406 pages )〕 which were among the key references on this new field of mathematics. He was a member of the editorial board of Journal of Graph Theory for two terms since inception and has been an elected fellow of the Institute of Combinatorics and its Applications since its foundation. Behzad has been one of the direct collaborators of late Paul Erdős, the second-most prolific mathematician of all time after Euler.〔(Y. Alavi, M. Behzad, Paul Erdös, D. R. Lick, ''Double vertex graphs'', J. Comb. Inf. Syst. Sci. 16, No.1, 37-50, 1991. )〕〔(A. Behzad, M. Behzad, and C. E. Praeger, ''On the Domination Number of the Generalized Petersen Graphs'', in journal of Discrete Mathematics, 308, 603-610, 2008. )〕〔(Arash Behzad, Mehdi Behzad and Cheryl Praeger, ''Basic Dominations in Graphs'', in Bulletin of the Institute of Combinatorics and its Applications (ICA), Volume 61, pp. 6-16, 2011 )〕〔(Mehdi Behzad, ''A characterization of total graphs'', in Proc. Amer. Math. Soc. 26, 383-389, 1970 )〕〔(Mehdi Behzad and Heydar Radjavi, ''Another analog of Ramsey numbers'', Math. Ann. 186, 228-232, 1970 )〕
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