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» Quadrangulations of Planar Sets
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CCCG
2003
13 years 8 months ago
On the Number of Pseudo-Triangulations of Certain Point Sets
We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double...
Oswin Aichholzer, David Orden, Francisco Santos, B...
TAMC
2009
Springer
14 years 1 months ago
Linear Kernel for Planar Connected Dominating Set
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...
Daniel Lokshtanov, Matthias Mnich, Saket Saurabh
GC
2010
Springer
13 years 5 months ago
Enumerative Properties of Rooted Circuit Maps
In 1966 Barnette introduced a set of graphs, called circuit graphs, which are obtained from 3-connected planar graphs by deleting a vertex. Circuit graphs and 3-connected planar g...
Zhicheng Gao, Han Ren
CCCG
2007
13 years 8 months ago
On the Number of Empty Pseudo-Triangles in Point Sets
We analyze the minimum and maximum number of empty pseudo-triangles defined by any planar point set. We consider the cases where the three convex vertices are fixed and where th...
Marc J. van Kreveld, Bettina Speckmann
IWPEC
2009
Springer
14 years 1 months ago
Planar Capacitated Dominating Set Is W[1]-Hard
Given a graph G together with a capacity function c : V (G) → N, we call S ⊆ V (G) a capacitated dominating set if there exists a mapping f : (V (G) \ S) → S which maps every...
Hans L. Bodlaender, Daniel Lokshtanov, Eelko Penni...