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From Encyclopedia Britannica http://www.britannica.com/EBchecked/topic/1443932/Avraham-Trahtman:

Avraham Trahtman Israeli mathematician

born

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.

Encyclopedia Britannica Australia.

Wikipedia (English, German, Russian, France
…)

MacTutor History of Mathematics, Biographies

http://www.techhap.com/sciencehistory/279150.html#.Wb5ddbIjFMv

Wolfram Research Mathematica

Israeli Mathematicians: Adi
Shamir, Giulio Racah, Saharon Shelah,

Zlil Sela, Robert Aumann, Michael
O. Rabin, Oded Schramm, Avraham Trahtman

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

Den sidste gode mand A.J.
kazinski, Politiken. 2010 (18
translations)

**The Last Good Man** A.J. Kazinski** Translated by:** Tiina
Nunnally **Simon @Schuster 2010**

Die Auserwählten von A.J. kazinski, Krimi-couch, 2011

А. Й.
Казински.
Последний
праведник. :
Астрель, 2012.

Arthur Benjamin, Gary Chartrand & Ping Zhang

__The Fascinating World of Graph Theory__

Popular Math., press.princeton.edu, 360, 2015

New Scientist, 186 (2495), 2005, London

Pearce F., Pyramids of dew 52-53

**Наука
и жизнь** 2020 **№ 2**

Максимов

**Универсальный
алгоритм**

, NEW YORK TIMES

Published: April 24,
1988 DAVID K. SHIPLER

Excerpts from some
recently published letters

Ogonyok, No. 15 April
1988 A. Trakhtman

Timeline Israel 1961-1995 (1970)

Timelines (1970)

Who'sWho in the World. 2006-2008

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

Dictionary of International Biography

33th Ed., London, 2006

The Times (

The Guardian
(Friday

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

The.

Haaretz Newspaper (

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

http://avva.livejournal.com/2260452.html

and other information in dozen of languages

CURRICULUM VITAE

Prof. Dr.
Avraham Trahtman

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, Sverdlovsk
Pedagogical University, Department of Mathematics.

1969-1984 From assistant to associate professor, Department of Computational
Mathematics, Ural Technical University.

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

Languages

English, German, Hebrew, Russian, Polish.