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GD
2001
Springer
15 years 2 months ago
Orthogonal Drawings with Few Layers
In this paper, we study 3-dimensional orthogonal graph drawings. Motivated by the fact that only a limited number of layers is possible in VLSI technology, and also noting that a s...
Therese C. Biedl, John R. Johansen, Thomas C. Sher...
SODA
2012
ACM
213views Algorithms» more  SODA 2012»
13 years 5 days 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
2008
IEEE
15 years 4 months ago
Dynamic Connectivity: Connecting to Networks and Geometry
Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in a...
Timothy M. Chan, Mihai Patrascu, Liam Roditty
IWPEC
2009
Springer
15 years 4 months ago
Paths of Bounded Length and Their Cuts: Parameterized Complexity and Algorithms
We study the parameterized complexity of two families of problems: the bounded length disjoint paths problem and the bounded length cut problem. From Menger’s theorem both proble...
Petr A. Golovach, Dimitrios M. Thilikos
GD
2007
Springer
15 years 3 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