25 years of the Electronic Journal of Combinatorics II Org: Richard A. Brualdi, Bruce Sagan, Maya Stein and David Wood [PDF]
FAN CHUNG, University of California, San Diego, United States Problems in spectral graph theory [PDF]
I will talk about several problems in spectral graph theory that I love to see solved.
ZDENĚK DVOŘÁK, Charles University, Czech Republic On triangle-free planar graphs [PDF]
Since the celebrated result of Grötzsch, the class of triangle-free planar graphs has attracted much attention. We will survey some of the recent results and open problems regarding this class.
BOJAN MOHAR, Simon Fraser University, Canada Crossing-critical graphs [PDF]
A graph $G$ is $c$-crossing-critical if $cr(G)\ge c$, but $cr(G-e) < c$ for every $e\in E(G)$, where $cr(.)$ denotes the crossing number of the corresponding graph. The speaker will present an overview about the ``tile" structure and generation process of graphs that are $c$-crossing-critical. This is joint work with Zden\v ek Dvo\v r\'ak and Petr Hlin\v en\'y.
JÓZSEF SOLYMOSI, University of British Columbia, Canada Rigidity of planar arrangements [PDF]
We will analyse various geometric problems, where we expect that overdetermined systems have certain rigidity. For example any planar joint-bar realization of a dense graphs has a rigid sub-framework, unless many joints are collinear. Or, if a point-line arrangement has many incidences, then it has a large sub-arrangement which has small degree of freedom. We will see how such rigidity concepts might help in solving classical problems in Discrete Geometry.