New and Old Graph Dimension Parameters

演讲人: Prof.Martin Charles Golumbic University of Haifa, Israel
时间: 2015-05-21 13:30-2015-05-21 14:30
地点:Room 102, Tsinghua Xuetang

In this talk, we will explore various intersection and containment based representations of graphs and posets along with their associated parameters. Among these are the boxicity and cubicity of graphs, the dimension and interval dimension of posets and their comparability graphs, the bending number of intersecting paths on a grid, and the grid dimension of a graph.

We will also present recent work on the new notions of the separation dimension of a graph and the induced separation dimension of a graph. One of our main aims has been to find significant interconnections between such dimensional parameters. For example, we establish bounds relating the bending number to the partial order dimension for co-comparability graphs, and relating the induced separation dimension with the separation dimension and boxicity.


Martin Charles Golumbic is Professor of Computer Science and Director of the Caesarea Edmond Benjamin de Rothschild Institute for Interdisciplinary Applications of Computer Science at the University of Haifa. He is the founding Editor-in-Chief of the journal “Annals of Mathematics and Artificial Intelligence” and is or has been a member of the editorial boards of several other journals including “Discrete Applied Mathematics”, “Constraints” and “AI Communications”. His current area of research is in combinatorial mathematics interacting with real world problems in computer science and artificial intelligence. 

Professor Golumbic received his Ph.D. in mathematics from Columbia University in 1975 under the direction of Samuel Eilenberg. He has held positions at the Courant Institute of Mathematical Sciences of New York University, Bell Telephone Laboratories, the IBM Israel Scientific Center and Bar-Ilan University. He has also had visiting appointments at the Université de Paris, the Weizmann Institute of Science, Ecole Polytechnique Fédérale de Lausanne, Universidade Federal do Rio de Janeiro, Rutgers University, Columbia University, Hebrew University and Tsinghua University.

He is the author of the book  “Algorithmic Graph Theory and Perfect Graphs”, coauthor of a second book “Tolerance Graphs” and has written many research articles in the areas of combinatorial mathematics, algorithmic analysis, expert systems, artificial intelligence, and programming languages. He has been a guest editor of special issues of several journals, the editor of the books “Advances in Artificial Intelligence, Natural Language and Knowledge-based Systems”, and “Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications”. His most recent book is “Fighting Terror Online: The Convergence of Security, Technology, and the Law”, published by Springer-Verlag.

Prof. Golumbic and was elected as Foundation Fellow of the Institute of Combinatorics and its Applications in 1995, and has been a Fellow of the European Artificial Intelligence society ECCAI since 2005.  He is a member of the Academia Europaea, honoris causa -- elected 2013. Martin Golumbic has been the chairman of over fifty national and international symposia. He a member of the Phi Beta Kappa, Pi Mu Epsilon, Phi Kappa Phi, Phi Eta Sigma honor societies and is married and the father of four bilingual, married daughters and has four granddaughters and five grandsons.