25 years of the Electronic Journal of Combinatorics II
Org: Richard A. Brualdi, Bruce Sagan, Maya Stein et 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.