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» On the geometry of graphs with a forbidden minor
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DAM
2000
97views more  DAM 2000»
13 years 4 months ago
Algorithms and obstructions for linear-width and related search parameters
The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering e1;:::;er in such a way that for every i = 1;:::...
Dimitrios M. Thilikos
DM
2007
78views more  DM 2007»
13 years 4 months ago
Properties of vertex cover obstructions
We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O(k-VERTEX COVER) and call it...
Michael J. Dinneen, Rongwei Lai
ISAAC
2010
Springer
230views Algorithms» more  ISAAC 2010»
13 years 2 months ago
Seidel Minor, Permutation Graphs and Combinatorial Properties
A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at a vertex v consists in complementing the ed...
Vincent Limouzy
COMBINATORICS
2002
87views more  COMBINATORICS 2002»
13 years 4 months ago
Map Genus, Forbidden Maps, and Monadic Second-Order Logic
A map is a graph equipped with a circular order of edges around each vertex. These circular orders represent local planar embeddings. The genus of a map is the minimal genus of an...
Bruno Courcelle, V. Dussaux
EJC
2007
13 years 4 months ago
Quickly deciding minor-closed parameters in general graphs
We construct algorithms for deciding essentially any minor-closed parameter, with explicit time bounds. This result strengthens previous results by Robertson and Seymour [1,2], Fr...
Erik D. Demaine, Mohammad Taghi Hajiaghayi