论文标题
在目标卵石上的猜想
On the Target Pebbling Conjecture
论文作者
论文摘要
Graph Pebbling是一个网络优化模型，用于满足顶点供应（称为卵石）的顶点需求，而在运输中部分卵石损失。图中需求的卵石数是最小的数字，许多供应鹅卵石的每个位置都满足了需求。目标猜想（Herscovici-Hester-Hurlbert，2009年）认为，当需求完全堆叠在一个顶点上时，就会发生固定尺寸$ t $的需求的最大卵石数量。这种猜想的真相对于攻击图形卵石中的许多开放问题可能很有用，包括涉及图形产品的格雷厄姆（Graham，1989）的著名猜想。它已经过验证，可用于完整的图表，周期，立方体和树木。在本文中，我们证明了对2个记录的猜想，并在成对上进行了旋转图。
Graph pebbling is a network optimization model for satisfying vertex demands with vertex supplies (called pebbles), with partial loss of pebbles in transit. The pebbling number of a demand in a graph is the smallest number for which every placement of that many supply pebbles satisfies the demand. The Target Conjecture (Herscovici-Hester-Hurlbert, 2009) posits that the largest pebbling number of a demand of fixed size $t$ occurs when the demand is entirely stacked on one vertex. This truth of this conjecture could be useful for attacking many open problems in graph pebbling, including the famous conjecture of Graham (1989) involving graph products. It has been verified for complete graphs, cycles, cubes, and trees. In this paper we prove the conjecture for 2-paths and Kneser graphs over pairs.
