图 Pebbling 的棒棒糖与立方权重函数
Lollipop and Cubic Weight Functions for Graph Pebbling
AI总结：
本文通过为四维立方体构造非树权重函数改进图 pebbling 数上界方法，提出 n 维立方体权重函数猜想，并为棒棒糖图变体构造有效权重函数。
摘要：
给定图 $G$ 顶点上的一种石子配置，一次 pebbling 移动从某个顶点移除两颗石子，并在相邻顶点放置一颗石子。图 $G$ 的 pebbling 数是指所需的最少石子数，使得给定任意初始石子配置，都能通过一系列 pebbling 移动将一颗石子移动到 $G$ 的任意顶点。通过为 $Q_4$ 构造一个非树权重函数，我们改进了由 Hurlbert 引入并由 Cranston 等人扩展的权重函数技术，该技术给出图 pebbling 数的上界。随后，我们针对 $n$ 维立方体提出一个关于权重函数的猜想。我们还为棒棒糖图的各种变体构造了一组有效权重函数，扩展了先前已知的构造。
英文摘要：
Given a configuration of pebbles on the vertices of a graph $G$, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph $G$ is the smallest number of pebbles required such that, given an arbitrary initial configuration of pebbles, one pebble can be moved to any vertex of $G$ through some sequence of pebbling moves. Through constructing a non-tree weight function for $Q_4$, we improve the weight function technique, introduced by Hurlbert and extended by Cranston et al., that gives an upper bound for the pebbling number of graphs. Then, we propose a conjecture on weight functions for the $n$-dimensional cube. We also construct a set of valid weight functions for variations of lollipop graphs, extending previously known constructions.
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。
