Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, November 01, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Alexander Engström

Playing with independent sets

A subset of the vertex set of a graph is independent if its induced subgraph has no edges.

Given a graph, a game is played between an angel and the devil. The goal of the angel is to determine if a set of vertices is independent or not, without knowing exactly which vertices are in the set. When they start the angel knows nothing, but she can ask the devil if vertices are in the set or not. The devil wins if the angel asks about the complete vertex set.

Strategies for the angel, and how much she must cheat to win, give information about a topological space constructed from the independent sets, called the independence complex. Using this game we get easier proofs and generalize recent results by Ehrenborg and Hetyei on independence complexes of trees, and work by Kalai and Meshulam on independence complexes of graphs with degree restrictions. Also, this game gives a combinatorial proof of a theorem on chessboard complexes by Björner and Lovász.

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