Examples

We have made conjectures for the following objects, among others.

  1. Upper and lower bounds for the independence number of a graph.
  2. Upper and lower bounds for the determinant of a matrix.
  3. Necessary and sufficient conditions for whether a graph contains a hamilton cycle.
  4. Upper and lower bounds for various invariants associated with the game Chomp.
  5. Lower bounds for Goldbach(x), the number of ways to represent x as a sum of primes.

 

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3 thoughts on “Examples

  1. someone knows a non-efficient characterization of graphs where the independence number \alpha equals the Lovász \vartheta function?

  2. No. This would also be of interest. An efficient characterization, though, would give a new and possible large class of graphs where \alpha can be computed efficiently. Expanding this class is the immediate goal of this project.

  3. Thanks. A non-efficient characterization is interesting for “my” problem :) but an efficient characterization is more interesting

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