## On approximate graph colouring and MAX-k-CUT algorithms based on the θ-function (2002)

Citations: | 17 - 1 self |

### BibTeX

@MISC{Klerk02onapproximate,

author = {E. de Klerk and D. V. Pasechnik and J. P. Warners},

title = {On approximate graph colouring and MAX-k-CUT algorithms based on the θ-function},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

The problem of colouring a k-colourable graph is well-known to be NP-complete, for k 3. The MAX-k-CUT approach to approximate k-colouring is to assign k colours to all of the vertices in polynomial time such that the fraction of `defect edges' (with endpoints of the same colour) is provably small. The best known approximation was obtained by Frieze and Jerrum [9], using a semidefinite programming (SDP) relaxation which is related to the Lovasz #-function. In a related work, Karger et al. [18] devised approximation algorithms for colouring k-colourable graphs exactly in polynomial time with as few colours as possible. They also used an SDP relaxation related to the #-function.