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From Encyclopedia Britannica:

**
Avraham Trahtman Israeli mathematician **

born
Feb. 10, 1944, Kalinovo,

http://www.britannica.com/EBchecked/topic-art/1443932/114969/Avraham-Trahtman

The astonishing news emerged in 2008 that in September 2007 a 63-year-old Israeli mathematician, Avraham Trahtman, had solved a long-standing problem in graph theory. The road-colouring conjecture, as it was known before being solved by Trahtman, was first suggested in 1970 by the Israeli-American mathematician Benjamin Weiss and the American mathematicians Roy L. Adler and L. Wayne Goodwyn. The theorem concerns a special type of graph, or network, that fulfills certain conditions. The network must have a finite number of vertices (specific locations, or points) and directed edges (one-way paths), be strongly connected (a path must exist from any vertex a to any other vertex b and a path from b to a), and aperiodic (essentially, the cycles, or complete routes following different directions, must be independent). The road-colouring theorem asserts that for such a network, there always exists a synchronized colouring, or method of labeling the edges, to create a map with a simple set of directions, possibly involving many repetitions of the directions, that will lead from any starting point to any other given point. In other words, by following simple directions, such as to take a “red-blue-red” path, it is possible to start from any location and be certain to end up at the desired destination. The existence of such “universal maps” has theoretical implications for real-life problems in computer science, though having a universal map is not the same as having the most efficient route for any individual case.

Trahtman earned an undergraduate degree (1967) and a graduate degree
(1973) in mathematics from

Trahtman’s solution is notable for its brevity: at less than eight pages it is extremely concise and considered quite elegant. The proof is also rather noteworthy in that most major mathematical breakthroughs come from individuals before the age of 40, or even 30. Trahtman proved, however, that age was not a barrier to solving a nearly 40-year-old mathematical conundrum.

Encyclopedia Britannica

MacTutor History of
Mathematics, Biographies

Wolfram Research Mathematica

Publisher: Books LLC
(Editor) (September 15, 2010) ISBN-10: 1156843480

Timeline

Timelines (1970)

New Scientist, 186 (2495), 2005, London

Pearce F., Pyramids of dew 52-53

Who'sWho in the World. 2006-2008

Marquis Who's Who, 23th-28th Ed., NY

Dictionary of International Biography

33th Ed.,

The Times (4 March 2009). M du Sautoy, Sexy maths: ditch the GPS, just follow
the colour code,

The Guardian (Friday 21 March 2008). A
Heller, Security guard solves 38-year-old maths poser,

The Telegraph (21 March 2008). R
Highfield, Directions from anywhere: maths problem solved,

The.

Haaretz Newspaper
(20 March 2008).Israeli ex-security guard solves 38-year-old math problem

Math in Media, AMS, 03.08

Associated Press, Aron Heller, 20.03.08

The Canadian Press,
Aron Heller, 20.03.08

Ediot ahronot, N.
Mozgovaja, 06.02.08

International Herald Tribune, 20.03 08

BBC News,
spanish, Mundo, 12.02.08

The Herald,
22.03.08

Math Gateway of
AMS, 25.02.08

IsraelNN, AruzSheva, Hillel Fendel,
07.02.08

The Epoch Times,
in

Physics Today, 21.03.08

Millennium Mathematics Project,

Hacofe, Hadar
Rabid, 24.02.08

Evreiskij mir USA, 08.02.08

BecomingJewish, 10.02.08

IsRealli, Israel official, 14.02.08

Israel 21C, Karin Kloosterman. 18 02 2008.

Neue Zürcher
Zeitung, George Szpiro, Wie man auf Irrwegen ans Ziel gelangt, 30.03.2008

Kristeling
Dagblat, 12.02.08

Red

CloudWatcher, 09.02.08

ProphecyNewsWatch,
09.02.08

Forex Times, 18.02.08

Lenta.ru,
09.02.08

Itogi, N9, Astakhova, 06.03.08

Nauka v sviti, Ukraina 22.03.08

Izvestia, D. Varlamova, 04.04.08

Novosti, 10.04.08

REN TV, 04.06.08

Belfast Telegraph 21.03.08

Contemporary Centrist, 21.03.08

Deccan Herald 21.03.08

Izmirdeyasam, 22.03.08

and other information in dozen of languages

CITATION of the
publications

ROAD COLORING, ArXiv
downloads

Academic interests

Algebra, finite automata, water problems, algorithms, computing.

Education

1962-1967 Ural State University,
Mathematics, degree II, 1967.

1970-1972 Ural State University, Mathematics, degree III,1973.

Work experience

1995- 2012

1994-1995 Hebrew University - Lecturer, Pre-education Department

1991-1992 Assistant professor,

1969-1984 From assistant to associate professor, Department of Computational
Mathematics,

Computing

Creation of package TESTAS for verification of local testability and its
generalizations (threshold, right, left, bilateral, piecewise and other) for
both transition graphs of automata and transition semigroups, for checking
synchronizability and finding synchronizing words, for finding transition
semigroup of automaton.

The C/C^{++} compact package TESTAS is mentioned on home pages of
several prominent CONFERENCES
among the embedded systems for manipulating automata.

See htpp://www.cs.biu.ac.il/~trakht/Testas.html

Languages

English, German, Hebrew, Russian, Polish.