Tomaž Pisanski | |
---|---|

Born | |

Nationality | Slovene |

Alma mater | University of Ljubljana, Pennsylvania State University |

Scientific career | |

Fields | Topological graph theory, Algebraic graph theory, Discrete mathematics, Configuration (geometry). |

Institutions | University of Primorska |

Doctoral advisor | Torrence Parsons |

**Tomaž (Tomo) Pisanski** (born May 24, 1949 in Ljubljana, Slovenia) is a Slovenian mathematician working mainly in discrete mathematics and graph theory. He is considered by many Slovenian mathematicians to be the "father of Slovenian discrete mathematics."^{ [1] }

As a high school student, Pisanski competed in the 1966 and 1967 International Mathematical Olympiads as a member of the Yugoslav team, winning a bronze medal in 1967.^{ [2] } He studied at the University of Ljubljana where he obtained a B.Sc, M.Sc and PhD in mathematics. His 1981 PhD thesis in topological graph theory was written under the guidance of Torrence Parsons. He also obtained an M.Sc. in computer science from Pennsylvania State University in 1979.^{ [3] }

Currently, Pisanski is a professor of discrete and computational mathematics and Head of the Department of Information Sciences and Technology at University of Primorska in Koper.^{ [4] } In addition, he is a Professor at the University of Ljubljana Faculty of Mathematics and Physics (FMF). He has been a member of the Institute of Mathematics, Physics and Mechanics (IMFM) in Ljubljana since 1980, and the leader of several IMFM research projects.^{ [5] } In 1991 he established the Department of Theoretical Computer Science at IMFM, of which he has served as both head and deputy head.

He has taught undergraduate and graduate courses in mathematics and computer science at the University of Ljubljana, University of Zagreb, University of Udine, University of Leoben, California State University, Chico, Simon Fraser University, University of Auckland and Colgate University.^{ [6] } Pisanski has been an adviser for M.Sc and PhD students in both mathematics and computer science. Notable students include John Shawe-Taylor (B.Sc in Ljubljana), Vladimir Batagelj, Bojan Mohar, Sandi Klavžar, and Sandra Sattolo (M.Sc in Udine).

Pisanski’s research interests span several areas of discrete and computational mathematics, including combinatorial configurations, abstract polytopes, maps on surfaces, chemical graph theory, and the history of mathematics and science. 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*.^{ [7] } 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.^{ [8] } With Brigitte Servatius he is the co-author of the book *Configurations from a Graphical Viewpoint* (2013).^{ [9] }

- Pisanski, T. Genus of Cartesian products of regular bipartite graphs, Journal of Graph Theory 4 (1), 1980, 31-42. doi:10.1002/jgt.3190040105
- Graovac, A., T. Pisanski. On the Wiener index of a graph, Journal of Mathematical Chemistry 8 (1),1991, 53-62. doi:10.1007/BF01166923
- Boben, M., B. Grunbaum, T. Pisanski, A. Zitnik, Small triangle-free configurations of points and lines, Discrete & Computational Geometry 35 (3), 2006, 405-427. doi:10.1007/s00454-005-1224-9
- Conder, M., I. Hubard, T. Pisanski. Constructions for chiral polytopes, Journal of the London Mathematical Society 77 (1), 2007, 115-129. doi:10.1112/jlms/jdm093
- Pisanski, T. A classification of cubic bicirculants, Discrete Mathematics 307 (3-5), 2007, 567-578. doi:10.1016/j.disc.2005.09.053

From 1998-1999, Pisanski was chairman of the Society of Mathematicians, Physicists and Astronomers of Slovenia (DMFA Slovenije); he was appointed an honorary member in 2015.^{ [10] } He is a founding member of the International Academy of Mathematical Chemistry, serving as its Vice President from 2007-2011.^{ [11] } In 2008, together with Dragan Marušič, he founded * Ars Mathematica Contemporanea,* the first international mathematical journal to be published in Slovenia.^{ [12] } In 2012 he was elected to the Academia Europaea.^{ [13] } He is currently president of the Slovenian Discrete and Applied Mathematics Society (SDAMS), the first Eastern European mathematical society not wholly devoted to theoretical mathematics to be accepted as a full member of the European Mathematical Society (EMS).^{ [14] }

In 2005, Pisanski was decorated with the **Order of Merit (Slovenia)**,^{ [15] } and in 2015 he received the Zois award for exceptional contributions to discrete mathematics and its applications.^{ [16] } In 2016, he received the Donald Michie and Alan Turing Prize for lifetime achievements in Information Science in Slovenia.^{ [17] }

**Vladimir Batagelj** is a Slovenian mathematician and an emeritus professor of mathematics at the University of Ljubljana. He is known for his work in discrete mathematics and combinatorial optimization, particularly analysis of social networks and other large networks.

**Dragan Marušič** is a Slovene mathematician. Marušič obtained his BSc in technical mathematics from the University of Ljubljana in 1976, and his PhD from the University of Reading in 1981 under the supervision of Crispin Nash-Williams.

In combinatorial mathematics, a **Levi graph** or **incidence graph** is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line. They are named for Friedrich Wilhelm Levi, who wrote about them in 1942.

In mathematics, a **toroidal graph** is a graph that can be embedded on a torus. In other words, the graph's vertices can be placed on a torus such that no edges cross.

In the mathematical field of graph theory, the **Gray graph** is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. It was discovered by Marion C. Gray in 1932 (unpublished), then discovered independently by Bouwer 1968 in reply to a question posed by Jon Folkman 1967. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive.

In graph theory, the **Cartesian product***G**H* of graphs *G* and *H* is a graph such that

**Geometric graph theory** in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are allowed to be arbitrary continuous curves connecting the vertices, thus it is "the theory of geometric and topological graphs".

In mathematics, and particularly geometric graph theory, a **unit distance graph** is a graph formed from a collection of points in the Euclidean plane by connecting two points by an edge whenever the distance between the two points is exactly one. Edges of unit distance graphs sometimes cross each other, so they are not always planar; a unit distance graph without crossings is called a **matchstick graph**.

In mathematics, specifically projective geometry, a **configuration** in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.

**Hamming graphs** are a special class of graphs named after Richard Hamming and used in several branches of mathematics and computer science. Let *S* be a set of *q* elements and *d* a positive integer. The Hamming graph *H*(*d*,*q*) has vertex set *S ^{d}*, the set of ordered

In geometry, an **edge** is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a **side**. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.

In graph theory, a branch of mathematics, the **Moser spindle** is an undirected graph, named after mathematicians Leo Moser and his brother William, with seven vertices and eleven edges. It is a unit distance graph requiring four colors in any graph coloring, and its existence can be used to prove that the chromatic number of the plane is at least four.

In the mathematical field of graph theory, the **Möbius–Kantor graph** is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph *G*(8,3): that is, it is formed by the vertices of an octagon, connected to the vertices of an eight-point star in which each point of the star is connected to the points three steps away from it.

In mathematics, there are two competing definitions for a **chiral polytope**. One is that it is a polytope that is chiral, meaning that it does not have mirror symmetry. By this definition, a polytope that lacks any symmetry at all would be an example of a chiral polytope.

In combinatorial mathematics, **LCF notation** or **LCF code** is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle itself includes two out of the three adjacencies for each vertex, and the LCF notation specifies how far along the cycle each vertex's third neighbor is. A single graph may have multiple different representations in LCF notation.

**Bojan Mohar** is a Slovenian and Canadian mathematician, working in graph theory. He is a professor of mathematics at the University of Ljubljana and the holder of a Canada Research Chair in graph theory at Simon Fraser University in Vancouver, British Columbia, Canada.

In geometry, a **Hanner polytope** is a convex polytope constructed recursively by Cartesian product and polar dual operations. Hanner polytopes are named after Olof Hanner, who introduced them in 1956.

**Sandi Klavžar**(born 5 February 1962) is a Slovenian mathematician working in the area of graph theory and its applications. He is a professor of mathematics at the University of Ljubljana.

**Brigitte Irma Servatius** is a mathematician specializing in matroids and structural rigidity. She is a professor of mathematics at Worcester Polytechnic Institute, and has been the editor-in-chief of the *Pi Mu Epsilon Journal* since 1999.

**Klavdija Kutnar** is a Slovene mathematician. She received her PhD at the University of Primorska (UP) in 2008. She is Rector of the University of Primorska.

- ↑ lea. "Elaboration on the expertise, objectives and contributions — Gregas".
*www.gregas.eu*. Retrieved 2019-04-23. - ↑
- ↑ "Pisanski Tomaž - Biografski koledar slovenskih matematikov, fizikov, astronomov".
*stanislavpirnat.si*. Retrieved 2019-04-25. - ↑ "Oddelki - UP FAMNIT".
*www.famnit.upr.si*(in Slovenian). Retrieved 2019-04-25. - ↑ "Oddelek za teoretično računalništvo — IMFM".
*www.imfm.si*. Retrieved 2019-04-25. - ↑ lea. "Tomaž Pisanski — Gregas".
*www.gregas.eu*. Retrieved 2019-04-26. - ↑ J.L. Gross and T.W. Tucker, Topological graph theory, Wiley Interscience, 1987
- ↑ Dimakopoulos, Vassilios V.; Palios, Leonidas; Poulakidas, Athanasios S. (2005). "On the Hamiltonicity of the Cartesian product".
*Inf. Proc. Lett*.**96**(2): 49–53. doi:10.1016/j.ipl.2005.05.016. - ↑ Pisanski, Tomaž; Servatius, Brigitte (2013),
*Configurations from a Graphical Viewpoint*, Springer, ISBN 9780817683641 . - ↑ "DMFA Slovenije".
*www.dmfa.si*. Retrieved 2019-04-25. - ↑ "IAMC".
*www.iamc-online.org*. Retrieved 2019-04-25. - ↑ "Slovenska revija med najboljšimi matematičnimi revijami na svetu".
*primorske novice*. 16 June 2016. Retrieved 24 April 2019. - ↑ at Academia Europaea, retrieved 2012-10-09.
- ↑ "Novice".
*sdams.si*(in Slovenian). Retrieved 2019-04-25. - ↑ "Order of Merit (Red za zasluge)".
- ↑ "2015 | Ministrstvo za izobraževanje, znanost in šport".
*www.mizs.gov.si*. Retrieved 2019-04-23. - ↑ "IS AWARDS".
*IS2019*. Retrieved 2019-04-25.

- Pisanski's CV
- "prof. dr. Tomaz Pisanski".
- Tomaž Pisanski at the Mathematics Genealogy Project
- International Academy of Mathematical Chemistry - List of Members
- Slovenian Academy of Engineering - List of Members
- Images of Knowledge: Tomaž Pisanski - RTV radio interview
- 8th European Congress of Mathematics website
- Maps ∩ Configurations ∩ Polytopes ∩ Molecules ⊆ Graphs: The mathematics of Tomaž Pisanski on the occasion of his 70th birthday
- Ars Mathematica Contemporanea website
- Slovenian Society for Discrete and Applied Mathematics (SDAMS) website

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