Tomaž Pisanski
Encyclopedia
Tomaž Pisanski (b. May 24, 1949 in Ljubljana, Slovenia) is a Slovenia
n mathematician
working mainly in graph theory
.
In 1980 he calculated the genus
of the Cartesian product
of any pair of connected, bipartite, d-valent graphs using a method that was later called the White-Pisanski method.
In 1982 Vladimir Batagelj
and Pisanski proved that the Cartesian product
of a tree and a cycle
is Hamiltonian if and only if no degree of the tree exceeds the length of the cycle. They also proposed a conjecture concerning cyclic hamiltonicity of graphs. Their conjecture was proved in 2005 by Dimakopoulos, Palios and Poulakidas.
Pisanski studied at the University of Ljubljana
where he obtained a B.Sc., M.Sc and Ph.D. in mathematics. He competed in the 1966 and 1967 International Mathematical Olympiad
s, winning a bronze medal in 1967.http://www.imocompendium.com/index.php?options=gl%7Cimotres&imetakm=Pisanski,%20Tomo&p=3999c32 His Ph.D. thesis from topological graph theory
was written under the guidance of Torrence Parsons
. During his undergraduate studies he was an exchange student at the University of Nancy, France
. He also obtained a M.Sc. in computer science
from the Pennsylvania State University
.
Currently, Pisanski is a professor of discrete
and computational mathematics
at the University of
Ljubljana
. Since 2004 he has held a joint position at University of Primorska
in Koper. He has taught undergraduate and graduate courses in mathematics and computer science at the University of Zagreb
, University of Udine
, University of Leoben
, California State University, Chico
, Simon Fraser University
, University of Auckland
and Colgate University
. From 1998-1999 he was chairman of the Society of Mathematicians, Physicists and Astronomers of Slovenia
. In 2005 he was decorated
with the Order of Merit (Slovenia), He is a founding member of the International Academy of Mathematical Chemistry
and from 2007-2011 its Vice President. He is a founding editor of the Ars Mathematica Contemporanea
.
Slovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working mainly in graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
.
In 1980 he calculated the genus
Genus
In biology, a genus is a low-level taxonomic rank used in the biological classification of living and fossil organisms, which is an example of definition by genus and differentia...
of the Cartesian product
Cartesian product of graphs
In graph theory, the Cartesian product G \square H of graphs G and H is a graph such that* the vertex set of G \square H is the Cartesian product V × V; and...
of any pair of connected, bipartite, d-valent graphs using a method that was later called the White-Pisanski method.
In 1982 Vladimir Batagelj
Vladimir Batagelj
Vladimir Batagelj is a Slovenian mathematician, born 1948 in Idrija, Slovenia, who works mainly in data analysis, discrete mathematics, combinatorial optimization and applications of IT in education....
and Pisanski proved that the Cartesian product
Cartesian product of graphs
In graph theory, the Cartesian product G \square H of graphs G and H is a graph such that* the vertex set of G \square H is the Cartesian product V × V; and...
of a tree and a cycle
Cycle graph
In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain. The cycle graph with n vertices is called Cn...
is Hamiltonian if and only if no degree of the tree exceeds the length of the cycle. They also proposed a conjecture concerning cyclic hamiltonicity of graphs. Their conjecture was proved in 2005 by Dimakopoulos, Palios and Poulakidas.
Pisanski studied at the University of Ljubljana
University of Ljubljana
The University of Ljubljana is the oldest and largest university in Slovenia. With 64,000 enrolled graduate and postgraduate students, it is among the largest universities in Europe.-Beginnings:...
where he obtained a B.Sc., M.Sc and Ph.D. in mathematics. He competed in the 1966 and 1967 International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
s, winning a bronze medal in 1967.http://www.imocompendium.com/index.php?options=gl%7Cimotres&imetakm=Pisanski,%20Tomo&p=3999c32 His Ph.D. thesis from topological graph theory
Topological graph theory
In mathematics topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs....
was written under the guidance of Torrence Parsons
Torrence Parsons
Torrence Douglas Parsons was an American mathematician.He worked mainly in graph theory, and is known for introducing a graph-theoretic view of pursuit-evasion problems . He obtained his Ph.D. from Princeton University in 1966 under the supervision of Albert W. Tucker.-Further reading:Memorial...
. During his undergraduate studies he was an exchange student at the University of Nancy, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
. He also obtained a M.Sc. in computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
from the Pennsylvania State University
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
.
Currently, Pisanski is a professor of discrete
Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
and computational mathematics
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
at the University of
University of Ljubljana
The University of Ljubljana is the oldest and largest university in Slovenia. With 64,000 enrolled graduate and postgraduate students, it is among the largest universities in Europe.-Beginnings:...
Ljubljana
Ljubljana
Ljubljana is the capital of Slovenia and its largest city. It is the centre of the City Municipality of Ljubljana. It is located in the centre of the country in the Ljubljana Basin, and is a mid-sized city of some 270,000 inhabitants...
. Since 2004 he has held a joint position at University of Primorska
University of Primorska
University of Primorska is the third university in Slovenia. It is located in Koper, Izola, and Portorož and is named for the Slovenian Littoral region , where it is located.-History:The very first efforts to found a university in the Littoral were made almost one hundred years ago,...
in Koper. He has taught undergraduate and graduate courses in mathematics and computer science at the University of Zagreb
University of Zagreb
The University of Zagreb is the biggest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of Southeastern Europe...
, University of Udine
University of Udine
The University of Udine is a university in the city of Udine . It was founded in 1978 as part of the reconstruction plan of Friuli after the earthquake in 1976...
, University of Leoben
University of Leoben
The University of Leoben, in the town of Leoben, Austria, is the country's university for mining, metallurgy, and materials.It was founded on 4 November 1840, as the Steiermärkisch-Ständische Montanlehranstalt in Styria, Austria's mining region. In 1848 Peter Tunner relocated the university to the...
, California State University, Chico
California State University, Chico
California State University, Chico is the second-oldest campus in the twenty-three-campus California State University system. It is located in Chico, California, about ninety miles north of Sacramento...
, Simon Fraser University
Simon Fraser University
Simon Fraser University is a Canadian public research university in British Columbia with its main campus on Burnaby Mountain in Burnaby, and satellite campuses in Vancouver and Surrey. The main campus in Burnaby, located from downtown Vancouver, was established in 1965 and has more than 34,000...
, University of Auckland
University of Auckland
The University of Auckland is a university located in Auckland, New Zealand. It is the largest university in the country and the highest ranked in the 2011 QS World University Rankings, having been ranked worldwide...
and Colgate University
Colgate University
Colgate University is a private liberal arts college in Hamilton, New York, USA. The school was founded in 1819 as a Baptist seminary and later became non-denominational. It is named for the Colgate family who greatly contributed to the university's endowment in the 19th century.Colgate has 52...
. From 1998-1999 he was chairman of the Society of Mathematicians, Physicists and Astronomers of Slovenia
Society of Mathematicians, Physicists and Astronomers of Slovenia
The Society of Mathematicians, Physicists and Astronomers of Slovenia is the main Slovene society in the field of mathematics, physics and astronomy....
. In 2005 he was decorated
Civil decoration
A civil decoration is a decoration awarded to civilians for distinguished service. Military personnel might also be eligible for services of a non-military nature...
with the Order of Merit (Slovenia), He is a founding member of the International Academy of Mathematical Chemistry
International Academy of Mathematical Chemistry
The International Academy of Mathematical Chemistry was founded in Dubrovnik in 2005 by Milan Randic. The Academy Members are 88 from all over the world , comprising six scientists awarded the Nobel Prize....
and from 2007-2011 its Vice President. He is a founding editor of the Ars Mathematica Contemporanea
Ars Mathematica Contemporanea
Ars Mathematica Contemporanea is a peer-reviewed scientific journal covering mathematics and published by the Society of Mathematicians, Physicists and Astronomers of Slovenia, Slovenia, together with the Institute of Mathematics, Physics, and Mechanics and the University of Primorska. It is...
.