文章基本信息

标题：Lower Bounds for Electrical Reduction on Surfaces
本地全文：下载
作者：Hsien-Chih Chang ; Marcos Cossarini ; Jeff Erickson 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：129
页码：1-16
DOI：10.4230/LIPIcs.SoCG.2019.25
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We strengthen the connections between electrical transformations and homotopy from the planar setting - observed and studied since Steinitz - to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the number of electrical transformations required to reduce an n-vertex graph on surface in the worst case [SOCG 2016] in two different directions. Our previous Omega(n^{3/2}) lower bound applies only to facial electrical transformations on plane graphs with no terminals. First we provide a stronger Omega(n^2) lower bound when the planar graph has two or more terminals, which follows from a quadratic lower bound on the number of homotopy moves in the annulus. Our second result extends our earlier Omega(n^{3/2}) lower bound to the wider class of planar electrical transformations, which preserve the planarity of the graph but may delete cycles that are not faces of the given embedding. This new lower bound follow from the observation that the defect of the medial graph of a planar graph is the same for all its planar embeddings.
关键词：electrical transformation; Delta-Y-transformation; homotopy; tight; defect; SPQR-tree; smoothings; routing set; 2-flipping