ROAD COLORING, ArXiv downloads

Listings & Recognitions of results

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

Wikipedia
(English, German, Russian, France …)

MacTutor
History of Mathematics, Biographies

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

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

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., 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

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,

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

Languages

English, German, Hebrew, Russian, Polish.