• Corpus ID: 235490455

An eigenvalue bound for the fractional chromatic number

  title={An eigenvalue bound for the fractional chromatic number},
  author={Marcel Kenji de Carli Silva and Gabriel Coutinho and Rafael Grandsire},
We show that Hoffman’s sum of eigenvalues bound for the chromatic number is at least as good as the Lovász theta number, but no better than the ceiling of the fractional chromatic number. In order to do so, we display an interesting connection between this sum of eigenvalues bound and a generalization of the Lovász theta number introduced by Manber and Narasimhan in 1988. 

Tales of Hoffman: Three extensions of Hoffman's bound on the graph chromatic number

Colouring the Normalized Laplacian

Eigenvalue bounds for independent sets

New Spectral Bounds on the Chromatic Number Encompassing all Eigenvalues of the Adjacency Matrix

The purpose of this article is to improve existing lower bounds on the chromatic number chi by using a new technique of converting the adjacency matrix into the zero matrix by conjugating with unitary matrices and use majorization of spectra of self-adjoint matrices.

Interlacing eigenvalues and graphs

On the Shannon capacity of a graph

  • L. Lovász
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 1979
It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.

Spectral Lower Bounds for the Orthogonal and Projective Ranks of a Graph

It is proved that many spectral lower bounds for the chromatic number, $\chi$, are also lower bound for the orthogonal rank of a graph, and it is conjectured that a stronger inertial lower Bound for $\xi$ is also a lower boundfor $\xi_f".

Relaxations of vertex packing

The Sandwich Theorem

  • D. Knuth
  • Mathematics
    Electron. J. Comb.
  • 1994
This report contains expository notes about a function vartheta(G), popularly known as the Lovasz number of a graph G, that can be computed efficiently, although it lies "sandwiched" between other classic graph numbers whose computation is NP-hard.

Eigenvalues in Combinatorial Optimization

In the last decade many important applications of eigenvalues and eigenvectors of graphs in combinatorial optimization were discovered. The number and importance of these results is so fascinating