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ENDM
2007
68views more  ENDM 2007»
14 years 11 months ago
List Colouring Squares of Planar Graphs
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3
Frédéric Havet, Jan van den Heuvel, ...
SIAMCOMP
2008
77views more  SIAMCOMP 2008»
14 years 11 months ago
A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights
We give an algorithm requiring O(c1/2 n) time to find an -optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edgele...
Philip N. Klein
JCT
2007
77views more  JCT 2007»
14 years 11 months ago
Exponentially many 5-list-colorings of planar graphs
We prove that every planar graph with n vertices has at least 2n/9 distinct list-colorings provided every vertex has at least five available colors. © 2006 Elsevier Inc. All rig...
Carsten Thomassen
SIAMDM
2008
86views more  SIAMDM 2008»
14 years 11 months ago
Hamilton Cycles in Planar Locally Finite Graphs
A classical theorem by Tutte assures the existence of a Hamilton cycle in every finite 4-connected planar graph. Extensions of this result to infinite graphs require a suitable co...
Henning Bruhn, Xingxing Yu
CORR
2011
Springer
173views Education» more  CORR 2011»
14 years 6 months ago
Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in O(diameter*n*log(n)) Time
We develop a new technique for computing maximum flow in directed planar graphs with multiple sources and a single sink that significantly deviates from previously known techniqu...
Philip N. Klein, Shay Mozes