图卵石的棒棒糖和立方权函数

IF 0.9 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Journal of Combinatorial Optimization Pub Date : 2024-12-25 DOI:10.1007/s10878-024-01248-1
Marshall Yang, Carl Yerger, Runtian Zhou
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引用次数: 0

摘要

给定图G顶点上的鹅卵石配置,鹅卵石移动从一个顶点移除两个鹅卵石,并在相邻顶点上放置一个鹅卵石。图G的鹅卵石数是鹅卵石的最小数量,给定鹅卵石的任意初始配置,一个鹅卵石可以通过一些鹅卵石移动序列移动到G的任何顶点。通过构造\(Q_4\)的非树权函数,我们改进了由Hurlbert引入并由Cranston等人扩展的权函数技术,该技术给出了图的铺位数的上界。然后,我们提出了n维立方体的权函数猜想。我们还为棒棒糖图的变化构造了一组有效的权函数,扩展了以前已知的结构。
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Lollipop and cubic weight functions for graph pebbling

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.

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来源期刊
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization 数学-计算机:跨学科应用
CiteScore
2.00
自引率
10.00%
发文量
83
审稿时长
6 months
期刊介绍: The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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