论文标题
最低度确保超图是哈密顿量连接的
Minimum degree ensuring that a hypergraph is hamiltonian-connected
论文作者
论文摘要
如果对于任何不同的顶点$ x $和$ y $，$ h $，$ h $，$ h $ a Hypergraph $ h $与hamiltonian berge路径从$ x $到$ y $。我们发现所有$ 3 \ leq r <n $，最低度的$δ（n，r）$的精确下限，$ n $ vertex $ r $ r $ r $ rubiform-rustraph hypergraph $ h $，保证$ h $ h $是汉密尔顿连接的。事实证明，$ 3 \ leq n/2 <r <n $，$δ（n，r）$比保证存在哈密顿berge循环的学位少1个。此外，与图形不同，对于每一个$ r \ geq 3 $，都有$ r $均匀的超图，该超图与汉密尔顿连接，但不包含汉密尔顿的berge循环。
A hypergraph $H$ is hamiltonian-connected if for any distinct vertices $x$ and $y$, $H$ contains a hamiltonian Berge path from $x$ to $y$. We find for all $3\leq r<n$, exact lower bounds on minimum degree $δ(n,r)$ of an $n$-vertex $r$-uniform hypergraph $H$ guaranteeing that $H$ is hamiltonian-connected. It turns out that for $3\leq n/2<r<n$, $δ(n,r)$ is 1 less than the degree bound guaranteeing the existence of a hamiltonian Berge cycle. Moreover, unlike for graphs, for each $r \geq 3$ there exists an $r$-uniform hypergraph that is hamiltonian-connected but does not contain a hamiltonian Berge cycle.
