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» Existence and Construction of Edge Disjoint Paths on Expande...
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DAM
2008
84views more  DAM 2008»
13 years 5 months ago
Edge-splittings preserving local edge-connectivity of graphs
Let G = (V + s, E) be a 2-edge-connected graph with a designated vertex s. A pair of edges rs, st is called admissible if splitting off these edges (replacing rs and st by rt) pre...
Zoltán Szigeti
SODA
2012
ACM
213views Algorithms» more  SODA 2012»
11 years 8 months ago
Expanders are universal for the class of all spanning trees
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
FOCS
2009
IEEE
14 years 15 days ago
Distance Oracles for Sparse Graphs
Abstract— Thorup and Zwick, in their seminal work, introduced the approximate distance oracle, which is a data structure that answers distance queries in a graph. For any integer...
Christian Sommer 0002, Elad Verbin, Wei Yu
ECCC
2007
147views more  ECCC 2007»
13 years 5 months ago
Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs
In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal pairs and an integer c. The objective is to...
Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswa...
GD
2007
Springer
13 years 12 months ago
A Bipartite Strengthening of the Crossing Lemma
Let G = (V, E) be a graph with n vertices and m ≥ 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Ω(m3 /n2 ) pairs of crossing edges; or ...
Jacob Fox, János Pach, Csaba D. Tóth