论文标题
Buratti-Horak-Rosa的猜想适用于一些尺寸三大的基础集
The Buratti-Horak-Rosa Conjecture Holds for Some Underlying Sets of Size Three
论文作者
论文摘要
Buratti-Horak-Rosa的猜想涉及完整图中带有顶点标签的哈密顿路径的边缘标签的多组，$ 0，1，\ ldots，{v-1} $在特定的诱导边缘标签下。当构件集的基础集的大小最多为2时，已证明该猜想已被证明是$ \ {1,2,3,4 \} $的子集以及许多其他基础集的部分结果。我们使用可长期实现的方法表明，当$ \ max（u）\ leq 7 $或$ xyz \ leq 24 $时，每个基础设置$ u = \ = \ = \ = \ {x，y，z \} $的猜想所保留，并以$ u = = \ {1,2,11 \} $除外。我们还表明，对于任何$ x $，对于基础设置$ \ {1,2，x \} $的猜想的有效性均取决于猜想的有效性，用于有限的许多多机，并具有此基础集。
The Buratti-Horak-Rosa Conjecture concerns the possible multisets of edge-labels of a Hamiltonian path in the complete graph with vertex labels $0, 1, \ldots, {v-1}$ under a particular induced edge-labeling. The conjecture has been shown to hold when the underlying set of the multiset has size at most~2, is a subset of $\{1,2,3,4\}$ or $\{1,2,3,5\}$, or is $\{1,2,6\}$, $\{1,2,8\}$ or $\{1,4,5\}$, as well as partial results for many other underlying sets. We use the method of growable realizations to show that the conjecture holds for each underlying set $U = \{ x,y,z \}$ when $\max(U) \leq 7$ or when $xyz \leq 24$, with the possible exception of $U = \{1,2,11\}$. We also show that for any even $x$ the validity of the conjecture for the underlying set $\{ 1,2,x \}$ follows from the validity of the conjecture for finitely many multisets with this underlying set.
