具有循环2-相交格雷码的${\rm{TS}}(v,λ)$：$v\equiv 0$或$4\pmod{12}$
${\rm{TS}}(v,λ)$ with cyclic 2-intersecting Gray codes: $v\equiv 0$ or $4\pmod{12}$
摘要：
${\rm{TS}}(v,λ)$是一对$(V,\mathcal{B})$，其中$V$包含$v$点，而$\mathcal{B}$包含$V$的$3$元素子集，因此$V$中的每一对都精确地出现在$λ$块中。${\rm{TS}}(v,λ)$的$2$ -块相交图（$2$-BIG）是这样的图，其中每个顶点由来自${\rm{TS}}(v,λ)$的块表示，并且如果$|B_i\cap B_j|=2$，则每对块$B_i,B_j\in \mathcal{B}$由边连接。利用Schreiber给出的${\rm{TS}}(v,λ)$的结构，我们证明了对于$v\equiv 0$或$4\pmod{12}$，存在一个$2$ -BIG为Hamilton的${\rm{TS}}(v,λ)$.
英文摘要：
A ${\rm{TS}}(v,λ)$ 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 $λ$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\rm{TS}}(v,λ)$ is a graph where each vertex is represented by a block from the ${\rm{TS}}(v,λ)$ and each pair of blocks $B_i,B_j\in \mathcal{B}$ are joined by an edge if $|B_i\cap B_j|=2$. Using constructions for ${\rm{TS}}(v,λ)$ given by Schreiber, we show that there exists a ${\rm{TS}}(v,λ)$ for $v\equiv 0$ or $4\pmod{12}$ whose $2$-BIG is Hamiltonian.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
