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JCT
2006
134views more  JCT 2006»
13 years 7 months ago
MacLane's planarity criterion for locally finite graphs
MacLane's planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B....
Henning Bruhn, Maya Jakobine Stein
COMPGEOM
2010
ACM
14 years 15 days ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
ESA
2009
Springer
127views Algorithms» more  ESA 2009»
14 years 2 months ago
Maximum Flow in Directed Planar Graphs with Vertex Capacities
In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the...
Haim Kaplan, Yahav Nussbaum
FOCS
2008
IEEE
14 years 1 months ago
Embeddings of Topological Graphs: Lossy Invariants, Linearization, and 2-Sums
We study the properties of embeddings, multicommodity flows, and sparse cuts in minor-closed families of graphs which are also closed under 2-sums; this includes planar graphs, g...
Amit Chakrabarti, Alexander Jaffe, James R. Lee, J...
JNW
2008
75views more  JNW 2008»
13 years 7 months ago
Time Efficient Radio Broadcasting in Planar Graphs
Abstract-- We study the communication primitive of broadcasting (one-to-all communication) in known topology radio networks, i.e., where for each primitive the schedule of transmis...
Fredrik Manne, Qin Xin