Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, November 28, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Stefanie Gerke

Connectivity of random instances of addable graph classes

We call a non-empty class A of labelled graphs addable if for each graph G in A and any two vertices u and v in distinct components of G, the graph obtained by adding the edge {u,v} to G is in A. Examples of addable graph classes include forests, planar graphs, and triangle-free graphs. The set of graphs in A with vertex set {1,..,n} is denoted by A_n. McDiarmid, Steger, and Welsh conjecture that for an addable class of graphs with the property that A_n for all sufficiently large n, an element R_n drawn uniformly at random from A_n satisfies \liminf_{n\rightarrow \infty} P[R_n is connected] >= e^{-1/2}. Let us remark that one cannot increase e^{-1/2} as the class of forests shows.

McDiarmid, Steger, and Welsh proved the conjecture when e^{-1/2} is replaced by e^{-1}. We improve this constant to e^{-0.7983}. To prove this result we find for a>0, an upper bound on the generalized Randic index R_-a(T) of a tree T, that is, the sum over all edges {u,v} in E(T) of (d(u)d(v))^{-a}, where d(u) is the degree of u in T. Randic introduced this measure to give a theoretical characterization of molecular branching. For every a<0, we find an effectively computable constant b=b(a) such that for all trees T on n>2 vertices, R_{-a}(T)<= b(n+1). We also construct infinitely many trees such that R_{-a}(T)>= b(n-1).

Joint work with Paul Balister and Bela Bollobas.


Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks


Automatic MiSe System Software Version 1.4803M   |   admin login