Publication at Faculty of Mathematics and Physics |
2017
Abstract
The generalised colouring numbers col(r)(G) and wcol(r)(G) were introduced by Kierstead and Yang as a generalisation of the usual colouring number, and have since then found important theoretical and algorithmic applications. In this paper, we dramatically improve upon the known upper bounds for generalised colouring numbers for graphs excluding a fixed minor, from the exponential bounds of Grohe et al. to a linear bound for the r-colouring number col(r) and a polynomial bound for the weak r-colouring number wcol(r).