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Representation of a graph as a path graph "thickened" by some amount
bounded pathwidth, and the "vortices" appearing in the general structure theory for minor-closed graph families have bounded pathwidth. Pathwidth, and graphs
Pathwidth
Measure of branching complexity
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
Strahler_number
Number denoting a graph's closeness to a tree
the pathwidth may be defined from interval graphs analogously to the definition of treewidth from chordal graphs. As a consequence, the pathwidth of a
Treewidth
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
Glossary_of_graph_theory
Intersection graph for intervals on the real number line
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
Interval_graph
Graph with all vertices of degree 3
the largest possible pathwidth of an n {\displaystyle n} -vertex cubic graph? More unsolved problems in mathematics The pathwidth of any n-vertex cubic
Cubic_graph
Graph drawing with vertices in horizontal layers
the fact that the graphs that have drawings of this type have bounded pathwidth. For layered drawings of concept lattices, a hybrid approach combining
Layered_graph_drawing
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
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Node labeling problem in graph theory
vertices in G {\displaystyle G} . If a graph G has bandwidth k, then its pathwidth is at most k, and its tree-depth is at most k log(n/k). In contrast, as
Graph_bandwidth
Graph representing a permutation
the same size in the corresponding permutation graph. the treewidth and pathwidth of permutation graphs can be computed in polynomial time; these algorithms
Permutation_graph
solvable in polynomial time.) Modularity maximization Monochromatic triangle Pathwidth, or, equivalently, interval thickness, and vertex separation number Rank
List_of_NP-complete_problems
Chordal graph with the given graph as a subgraph
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
Chordal_completion
Problem of finding the longest simple path for a given graph
traversed by the search, to construct a path decomposition of the graph, with pathwidth d {\displaystyle d} . Apply dynamic programming to this path decomposition
Longest_path_problem
Finiteness of sets of forbidden graph minors
graph invariant bounded by some fixed constant; graphs with treewidth, pathwidth, or branchwidth bounded by some fixed constant. Some examples of finite
Robertson–Seymour_theorem
Measurement of graph sparsity
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
Degeneracy_(graph_theory)
Tree graph with all nodes within distance 1 from central path
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
Caterpillar_tree
Mapping of a graph into a tree
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
Tree_decomposition
Determining whether a knot is the unknot
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
Unknotting_problem
Connectivity measure in graph theory
Hafsteinsson, Hjálmtýr; Kloks, Ton (1995), "Approximating treewidth, pathwidth, frontsize, and shortest elimination tree", Journal of Algorithms, 18
Cycle_rank
Property in graph theory
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
Cutwidth
Numerical invariant of graphs
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
Tree-depth
Unrelated vertices in graphs
2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer
Independent set (graph theory)
Independent_set_(graph_theory)
Mathematical game/problem
invisible to the pursuers then the problem is equivalent to finding the pathwidth or vertex separation. Finding the number of pursuers necessary to capture
Pursuit–evasion
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
GNRS_conjecture
Type of algorithm
k of centers, the doubling dimension, the highway dimension, and the pathwidth. However, when combining k with the doubling dimension an EPAS exists
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Problem of grouping into triples
(2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer
3-dimensional_matching
Subgraph with contracted edges
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
Graph_minor
Gluing graphs at complete subgraphs
arbitrary subset of the other vertices) and vortices (graphs with low pathwidth that replace faces of the surface embedding). These characterizations
Clique-sum
Mathematical tree with cycle through leaves
Fedor V.; Thilikos, Dimitrios M. (2006), "A 3-approximation for the pathwidth of Halin graphs", Journal of Discrete Algorithms, 4 (4): 499–510, doi:10
Halin_graph
Intersection graph of unit intervals on the real line
the maximum clique. This property parallels similar relations between pathwidth and interval graphs, and between treewidth and chordal graphs. A weaker
Indifference_graph
Problem in computer science
2013). "Improved Approximation for 3-Dimensional Matching via Bounded Pathwidth Local Search". 2013 IEEE 54th Annual Symposium on Foundations of Computer
Set_packing
Points usable to draw any planar graph
into nested cycles, 2-outerplanar graphs and planar graphs of bounded pathwidth, have universal point sets of nearly-linear size. Planar 3-trees have
Universal_point_set
Theorem relating graph minors and topological embeddings
vortex is limited by a parameter called its depth, closely related to pathwidth. The reader may prefer to defer reading the following precise description
Graph_structure_theorem
Invariant in graph theory
(2002) for a weaker preliminary result, bounding the queue number by the pathwidth or by a combination of treewidth and degree. https://arxiv.org/pdf/1904
Queue_number
Graph which can be made planar by removing a single node
graph by replacing a bounded number of faces by "vortexes" of bounded pathwidth, as well as for other less precisely defined sets of graphs. An abstract
Apex_graph
Economical computational problem
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
Nash_equilibrium_computation
Also, for comparison, S1S can interpret connected graphs of bounded pathwidth. By contrast, for every set of graphs of unbounded treewidth, its existential
S2S_(mathematics)
Israeli professor of computer science (born 1953)
12.8158, doi:10.1006/jagm.1995.1047 Kaplan, Haim; Shamir, Ron (1996), "Pathwidth, Bandwidth, and Completion Problems to Proper Interval Graphs with Small
Ron_Shamir
time for an n {\displaystyle n} -vertex graph. For AT-free graphs, the pathwidth equals the treewidth. The strong perfect graph theorem holds for AT-free
Asteroidal_triple-free_graph
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Indian, Punjabi, Sikh
Living the Spiritual Way
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Bearer of High Ranking
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Derived from Lord Shiva
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English : from the Middle English personal name Ingelot, a pet form of any of various names such as Ingelbald ‘Angle bold’, Ingelbert ‘Angle bright’, or Ingelard ‘Angle hardy’. These were names of Germanic origin, introduced to Britain by the Normans or possibly by the Danish invaders a century earlier.
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Justice
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Vision, Propitious, Auspicious, Prudent, Bringer of glad tidings
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