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 A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, April 24, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Torsten Mütze

Antimagic Labellings of Graphs

An antimagic labelling of an undirected graph G=(V,E) is a bijective mapping from E to {1,2,...,|E|} such that all vertex sums are distinct, where a vertex sum is the sum of the labels of all edges incident with that vertex. A graph is called antimagic if it has an antimagic labelling. A conjecture of Ringel and Hartsfield from 1990 states that all connected graphs but K_2 are antimagic. In this talk we discuss antimagic labellings of directed graphs (here vertex sums are signed, counting labels of incoming edges positively and labels of outgoing edges negatively). There exists a variety of methods to prove antimagicness for certain graphs, from algorithmic to algebraic techniques (Combinatorial Nullstellensatz) and probabilistic methods (Lovász Local Lemma). We will put particular emphasis on these different techniques and highlight the relations between the directed and the undirected case.

Joint work with Dan Hefetz and Justus Schwartz.

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