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The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree
graph drawing planar graphs slopes planar slope number
2011/2/22
It is known that every planar graph has a planar embedding where edges are represented by non-crossing straight-line segments. We study the planar slope number, i.e., the minimum number of distinct ed...
Some results concerning the $p$-Royden and $p$-harmonic boundaries of a graph of bounded degree
p-Royden boundary p-harmonic boundary p-harmonic function
2011/1/20
Let p be a real number greater than one and let be a connected graph of bounded degree. We show that the p-Royden boundary of with the p-harmonic boundary removed is a F-set. We...
Drawing planar graphs of bounded degree with few slopes
planar graphs bounded degree few slopes
2010/12/1
settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists
a function f with the property that every planar graph G with maximum degree d admits a drawing
with nonc...
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time
Darboux polynomials rational first integrals bounded degree
2010/12/7
In this paper we study planar polynomial differential systems of this form: dX dt = ˙X = A(X, Y ),dY dt = ˙Y = B(X, Y ),where A,B ∈ Z[X, Y ] and deg A ≤ d, degB ≤ d, kAk1 ≤ H and kBk1 ≤H. A lot of pro...