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JCT
2006
134views more  JCT 2006»
14 years 9 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
15 years 2 months 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»
15 years 4 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
15 years 4 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»
14 years 9 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