$${\mathrm{TS}}(v,\lambda )$$ with Cyclic 2-Intersecting Gray Codes: $$v\equiv 0$$ or $$4\pmod {12}$$
| Autor: | Melissa S. Keranen, John Asplund |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Triple system
0211 other engineering and technologies 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology Intersection graph Lambda 01 natural sciences Hamiltonian path Graph Theoretical Computer Science Combinatorics Gray code symbols.namesake 010201 computation theory & mathematics symbols Discrete Mathematics and Combinatorics Mathematics |
| Zdroj: | Graphs and Combinatorics. 36:415-436 |
| ISSN: | 1435-5914 0911-0119 |
| DOI: | 10.1007/s00373-019-02107-1 |
| Popis: | A $${\mathrm{TS}}(v,{\lambda })$$ is a pair $$(V,\mathcal {B})$$ where V contains v points and $$\mathcal {B}$$ contains 3-element subsets of V so that each pair in V appears in exactly $${\lambda }$$ blocks. A 2-block intersection graph (2-BIG) of a $${\mathrm{TS}}(v,{\lambda })$$ is a graph where each vertex is represented by a block from the $${\mathrm{TS}}(v,{\lambda })$$ and each pair of blocks $$B_i,B_j\in \mathcal {B}$$ are joined by an edge if $$|B_i\cap B_j|=2$$. We show that there exists a $${\mathrm{TS}}(v,{\lambda })$$ for $$v\equiv 0$$ or $$4\pmod {12}$$ whose 2-BIG is Hamiltonian for all admissible $$(v,{\lambda })$$. This is equivalent to the existence of a $${\mathrm{TS}}(v,{\lambda })$$ with a cyclic 2-intersecting Gray code. |
| Databáze: | OpenAIRE |
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