报告题目：Balanced and circular chromatic number of signed graphs
报告人：Reza Naserasr教授，法国CNRS研究员（Université Paris Cité）
报告时间：2024年3月29日（周五）15:00-16:00
报告地点：20-306
报告摘要：The relation between minor theory and coloring is one of the most challenging areas of research in graph theory. In this talk we will try to develop notions that help to stablish a stronger connection between the two concepts. To this end, first we review the notion of signed graphs and minor theory for signed graphs. Then we present two notions of colorings for signed graphs: I. Balanced coloring, which is the minimum number of induced balanced sets to which vertices of a signed graph can be partitioned. II. Circular coloring of signed graphs, which is about mapping of the vertices to the points of a circle satisfying certain distance conditions depending on the sign of the edge. We then present signed Hadwiger conjecture and show that while seemingly it is a stronger conjecture than the original Hadwiger conjecture, in fact it is equivalent to it and has strong connection to the odd Hadwiger conjecture. This will be followed with some other results and plenty of open questions.
Key references:
[1] A. Jimenez, J. Mcdonald, R. Naserasr, K. Nurse, D. Quiroz, Balanced-chromatic number and Hadwiger-like conjectures. https://hal.science/hal-04174372
[2] R. Naserasr, Z. Wang, and X. Zhu, Circular chromatic number of signed graphs. Electron. J. Comb., 28(2):2, 2021.
报告人简介：Reza Naserasr教授于2004年获加拿大温哥华Simon Fraser大学博士学位，后于法国Bordeaux大学、加拿大Carleton大学和Waterloo大学做博士后研究，现任法国CNRS研究员（Université Paris Cité），主要研究图的染色和图的同态。