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ENDM
2007
68views more  ENDM 2007»
13 years 7 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»
13 years 7 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»
13 years 7 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»
13 years 7 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»
13 years 2 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