# Noon lecture

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On 10.05.2006 at 12:20 in S5, there is the following noon lecture:

# Edge-colourings of cubic graphs and partial Steiner triple

## Martin Škoviera

## Comenius University, Bratislava, Slovakia

## Abstract

Vizing's edge-colouring theorem divides cubic graphs into the class of 3-edge-colourable graphs (which comprises almost all of them) and a ``small" but annoying family of graphs that cannot be 3-edge-coloured. One possible approach to studying uncolourable cubic graphs consists in extending the definition of a 3-edge-colouring to include a wider class of cubic graphs. In this talk we propose a natural generalisation of the classical 3-edge-colouring based on the concept of a partial Steiner triple system. The colourings use points of the system as colours subject to the condition that any three colours meeting at a vertex form a triple. Many interesting systems occur as geometric configurations of points and lines, and the corresponding colourings seem to have a special importance.

In the talk we show that all bridgeless cubic graphs admit colourings by

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | future lectures)

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