Results 11 to 20 of about 1,027 (141)
Pathwidth of outerplanar graphs [PDF]
Journal of Graph Theory, 2006 AbstractWe are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a ...
Coudert, David +2 more
core +13 more sources
Tree-decompositions of small pathwidth [PDF]
Electronic Notes in Discrete Mathematics, 2001 The treewidth \(\text{ tw}(G)\) of \(G\) can be defined as minimum width of a tree-decomposition of \(G\), or minimum \(\omega(H)-1\) of a chordal triangulation \(H\) of \(G\). Similarely, the pathwidth \(\text{ pw}(G)\) can be defined via path-decompositions or triangulations into interval graphs. Thereby a path-decomposition is a tree-decomposition \(
Telle, Jan Arne
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Cycle decompositions of pathwidth‐6 graphs [PDF]
Journal of Graph Theory, Volume 94, Issue 2, Page 224-251, June 2020., 2020 Abstract Hajós' conjecture asserts that a simple Eulerian graph on n vertices can be decomposed into at most ⌊ ( n − 1 ) / 2 ⌋ cycles. The conjecture is only proved for graph classes in which every element contains vertices of degree 2 or 4. We develop new techniques to construct cycle decompositions.
Elke Fuchs +2 more
wiley +6 more sources
Pathwidth of Circular-Arc Graphs [PDF]
, 2007 The pathwidth of a graph G is the minimum clique number of H minus one, over all interval supergraphs H of G. Although pathwidth is a well-known and well-studied graph parameter, there are extremely few graph classes for which pathwidh is known to be tractable in polynomial time.
Karol Suchan, Ioan Todinca
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Approximating Pathwidth for Graphs of Small Treewidth [PDF]
ACM Transactions on Algorithms, 2021 We describe a polynomial-time algorithm which, given a graphGwith treewidtht, approximates the pathwidth ofGto within a ratio of\(O(t\sqrt {\log t})\). This is the first algorithm to achieve anf(t)-approximation for some functionf.Our approach builds on the following key insight: every graph with large pathwidth has large treewidth or contains a ...
Carla Groenland +3 more
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Circumference and Pathwidth of Highly Connected Graphs [PDF]
Journal of Graph Theory, 2014 AbstractBirmele [J Graph Theory 2003] proved that every graph with circumference t has treewidth at most . Under the additional assumption of 2‐connectivity, such graphs have bounded pathwidth, which is a qualitatively stronger conclusion. Birmele's theorem was extended by Birmele et al.
Emily Abernethy Marshall, David R. Wood
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On the Pathwidth of Planar Graphs [PDF]
, 2006 Fomin and Thilikos in [5] conjectured that there is a constant $c$ such that, for every $2$-connected planar graph $G$, {pw}(G^*) \leq 2\text{pw}(G)+c$ (the same question was asked simutaneously by Coudert, Huc and Sereni in [4]). By the results of Boedlander and Fomin [2] this holds for every outerplanar graph and actually is tight by Coudert, Huc and
Amini, Omid +2 more
core +6 more sources
The pathwidth and treewidth of cographs [PDF]
SIAM Journal on Discrete Mathematics, 1990 Summary: It is shown that the pathwidth of a cograph equals its treewidth, and a linear time algorithm to determine the pathwidth of a cograph and build a corresponding path-decomposition is given.
Hans L. Bodlaender, Rolf H. Möhring
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Exclusive Graph Searching vs. Pathwidth [PDF]
, 2014 In Graph Searching, a team of searchers aims at capturing an invisible fugitive moving arbitrarily fast in a graph. Equivalently, the searchers try to clear a contaminated network.The problem is to compute the minimum number of searchers required to ...
Markou, Euripides +2 more
core +5 more sources
Pathwidth vs Cocircumference [PDF]
SIAM Journal on Discrete MathematicsThe {\em circumference} of a graph $G$ with at least one cycle is the length of a longest cycle in $G$. A classic result of Birmelé (2003) states that the treewidth of $G$ is at most its circumference minus $1$. In case $G$ is $2$-connected, this upper bound also holds for the pathwidth of $G$; in fact, even the treedepth of $G$ is upper bounded by its
Marcin Briański +2 more
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