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» Diameter bounds for planar graphs
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IPL
2006
69views more  IPL 2006»
14 years 11 months ago
On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P
We show that computing the lexicographically first four-coloring for planar graphs is p 2hard. This result optimally improves upon a result of Khuller and Vazirani who prove this ...
André Große, Jörg Rothe, Gerd We...
JDA
2010
122views more  JDA 2010»
14 years 6 months ago
Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs
We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounde...
Ignasi Sau, Dimitrios M. Thilikos
APPROX
2008
Springer
89views Algorithms» more  APPROX 2008»
15 years 1 months ago
Quantum and Randomized Lower Bounds for Local Search on Vertex-Transitive Graphs
We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
Hang Dinh, Alexander Russell
COMGEO
2007
ACM
14 years 11 months ago
Graph drawings with few slopes
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-reg...
Vida Dujmovic, Matthew Suderman, David R. Wood
ARSCOM
2008
192views more  ARSCOM 2008»
14 years 12 months ago
Bounds on the metric and partition dimensions of a graph
Given a graph G, we say S V (G) is resolving if for each pair of distinct u, v V (G) there is a vertex x in S where d(u, x) = d(v, x). The metric dimension of G is the minimum c...
Glenn G. Chappell, John G. Gimbel, Chris Hartman