bounded pathwidth, and the "vortices" appearing in the general structure theory for minor-closed graph families have bounded pathwidth. Pathwidth, and graphs...

orientation and root) the pathwidth differs from the Strahler number, but is closely related to it: in a tree with pathwidth w and Strahler number s, these...

than its chromatic number), and the pathwidth of any graph G {\displaystyle G} is the same as the smallest pathwidth of an interval graph that contains...

the pathwidth may be defined from interval graphs analogously to the definition of treewidth from chordal graphs. As a consequence, the pathwidth of a...

The minimum width of any path decomposition of G is the pathwidth of G. pathwidth The pathwidth of a graph G is the minimum width of a path decomposition...

layer don't intersect. Therefore, one can see the relation to the pathwidth. Pathwidth restricted graphs are minor closed but the set of subgraphs of cyclically...

the fact that the graphs that have drawings of this type have bounded pathwidth. For layered drawings of concept lattices, a hybrid approach combining...

the largest possible pathwidth of an n {\displaystyle n} -vertex cubic graph? More unsolved problems in mathematics The pathwidth of any n-vertex cubic...

parameter derived from these special types of tree decompositions is known as pathwidth. A tree decomposition (X, T = (I, F)) of treewidth k is smooth, if for...

graph invariant bounded by some fixed constant; graphs with treewidth, pathwidth, or branchwidth bounded by some fixed constant. Some examples of finite...

theory under the name of structural cohesion. If a graph has treewidth or pathwidth at most k {\displaystyle k} , then it is a subgraph of a chordal graph...

edge-disjoint copies of the given graph. What is the largest possible pathwidth of an n-vertex cubic graph? The reconstruction conjecture and new digraph...

the same size in the corresponding permutation graph. the treewidth and pathwidth of permutation graphs can be computed in polynomial time; these algorithms...

traversed by the search, to construct a path decomposition of the graph, with pathwidth d {\displaystyle d} . Apply dynamic programming to this path decomposition...

polynomial time.) Modularity maximization Monochromatic triangle: GT6  Pathwidth, or, equivalently, interval thickness, and vertex separation number Rank...

Hafsteinsson, Hjálmtýr; Kloks, Ton (1995), "Approximating treewidth, pathwidth, frontsize, and shortest elimination tree", Journal of Algorithms, 18...

2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer...

his algorithm, but heuristically estimates it to be exponential in the pathwidth of a crossing diagram, which in turn is at most proportional to the square...

of the tree can be decomposed into. They are the connected graphs of pathwidth one. They are the connected triangle-free interval graphs. They are n-vertex...

invisible to the pursuers then the problem is equivalent to finding the pathwidth or vertex separation. Finding the number of pursuers necessary to capture...

k of centers, the doubling dimension, the highway dimension, and the pathwidth. However, when combining k with the doubling dimension an EPAS exists...

chordal completion whose maximum clique size is at most k + 1. It has pathwidth at most k if and only if G has at least one chordal completion that is...

equal to its tree-depth. More precisely, the treewidth is at most the pathwidth, which is at most one less than the tree-depth. A minor of a graph G {\displaystyle...

2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer...

(2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer...

excluded minors. For example a minor-closed graph family F has bounded pathwidth if and only if its forbidden minors include a forest, F has bounded tree-depth...

always at least as large as the treewidth or pathwidth of the same graph. However, it is at most the pathwidth multiplied by O ( Δ ) {\displaystyle O(\Delta...

its pathwidth is 2, but the same is true for any algorithm of the same kind. Finding a NE for a degree-3 graphical game with constant pathwidth and 2...

into nested cycles, 2-outerplanar graphs and planar graphs of bounded pathwidth, have universal point sets of nearly-linear size. Planar 3-trees have...

graphs and the graphs of bounded circuit rank, the graphs of bounded pathwidth, the 2-clique-sums of graphs of bounded size, and the k {\displaystyle...