10,366 research outputs found
Separators in High-Genus Near-Planar Graphs
Graph separators are a powerful tool that are motivated by divide and conquer algorithms on graphs. Results have shown the existence of separators in arbitrary planar graphs and other graphs with less restricted structure. This work explores planar separators and the planar separator theorem, as well as the existence of separators in the class of high genus near-planar graphs. These graphs have unbounded genus, where additionally the edges that cross each other are located near each other in the graph. Several different graph classes that are high genus near-planar graphs are investigated for their feasibility for an extended separator theorem result
Approximation Algorithms for Polynomial-Expansion and Low-Density Graphs
We study the family of intersection graphs of low density objects in low
dimensional Euclidean space. This family is quite general, and includes planar
graphs. We prove that such graphs have small separators. Next, we present
efficient -approximation algorithms for these graphs, for
Independent Set, Set Cover, and Dominating Set problems, among others. We also
prove corresponding hardness of approximation for some of these optimization
problems, providing a characterization of their intractability in terms of
density
On some simplicial elimination schemes for chordal graphs
We present here some results on particular elimination schemes for chordal
graphs, namely we show that for any chordal graph we can construct in linear
time a simplicial elimination scheme starting with a pending maximal clique
attached via a minimal separator maximal (resp. minimal) under inclusion among
all minimal separators
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