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Characterisation results for Steiner Triple Systems and their application to edge-colourings of cubic graphs
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Král', Daniel, Máčajová, Edita, Pór, Attila and Sereni, Jean-Sébastien (2010) Characterisation results for Steiner Triple Systems and their application to edge-colourings of cubic graphs. Canadian Journal of Mathematics, Vol.62 (No.2). pp. 355-381. doi:10.4153/CJM-2010-021-9 ISSN 0008-414X.
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Official URL: http://dx.doi.org/10.4153/CJM-2010-021-9
Abstract
It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations. Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective non-affine point-transitive Steiner triple system S.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Canadian Journal of Mathematics | ||||
Publisher: | University of Toronto Press | ||||
ISSN: | 0008-414X | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.62 | ||||
Number: | No.2 | ||||
Page Range: | pp. 355-381 | ||||
DOI: | 10.4153/CJM-2010-021-9 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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