Hamilton decompositions of block-intersection graphs of Steiner triple systems (Q2761052)
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scientific article; zbMATH DE number 1682914
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hamilton decompositions of block-intersection graphs of Steiner triple systems |
scientific article; zbMATH DE number 1682914 |
Statements
17 December 2001
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Steiner triple system
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block-intersection graph
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Hamilton decomposition
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0.9287762
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0.9034236
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0.8952937
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0.8945607
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0.8893739
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0.88759375
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Hamilton decompositions of block-intersection graphs of Steiner triple systems (English)
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Connect two triples of a Steiner triple system (STS) by an edge if they intersect. This is the block-intersection graph, and for STSs of order \(n\geq 19\) the author easily proves that an isomorphism of these graphs implies an isomorphism of the STSs (cliques of size \((n-1)/2\) identify points). The same result holds also for \(n\leq 15\), where some of the more difficult cases were proved with the help of computer. A computer was also used to verify that for \(n\leq 15\) block-intersection graphs of STSs are Hamilton decomposable.
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