A Steiner triple system which colors all cubic graphs
نویسندگان
چکیده
We prove that there is a Steiner triple system T such that every simple cubic graph can have its edges coloured by points of T in such a way that for each vertex the colours of the three incident edges form a triple in T . This result complements the result of Holroyd and Škoviera that every bridgeless cubic graph admits a similar colouring by any Steiner triple system of order greater than 3. The Steiner triple system employed in our proof has order 381 and is probably not the smallest possible.
منابع مشابه
Edge-colorings of cubic graphs with elements of point-transitive Steiner triple systems
A cubic graph G is S-edge-colorable for a Steiner triple system S if its edges can be colored with points of S in such a way that the points assigned to three edges Electronic Notes in Discrete Mathematics 29 (2007) 23–27 1571-0653/$ – see front matter © 2007 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2007.07.005 sharing a vertex form a triple in S. We sh...
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عنوان ژورنال:
- Journal of Graph Theory
دوره 46 شماره
صفحات -
تاریخ انتشار 2004