ISSN:
1573-7586
Keywords:
Steiner triple systems
;
derived triple systems
;
graphs
;
chromatic number
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We attach a graph to every Steiner triple system. The chromatic number of this graph is related to the possibility of extending the triple system to a quadruple system. For example, the triple systems with chromatic number one are precisely the classical systems of points and lines of a projective geometry over the two-element field, the Hall triple systems have chromatic number three (and, as is well-known, are extendable) and all Steiner triple systems whose graph has chromatic number two are extendable. We also give a configurational characterization of the Hall triple systems in terms of mitres.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008289721664
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