Results 41 to 50 of about 2,587 (156)
Superpatterns and Universal Point Sets [PDF]
, 2013 An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs.
A. Marcus +14 more
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Obstructions to within a few vertices or edges of acyclic [PDF]
, 1995 Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. It has been known for several years that, in principle, obstruction sets can be mechanically computed for most natural lower ideals.
Cattell, Kevin +2 more
core +3 more sources
On first-order transductions of classes of graphs [PDF]
Logical Methods in Computer ScienceWe study various aspects of the first-order transduction quasi-order on graph classes, which provides a way of measuring the relative complexity of graph classes based on whether one can encode the other using a formula of first-order (FO) logic.
Samuel Braunfeld +3 more
doaj +1 more source
Discrete Mathematics & Theoretical Computer ScienceNot every directed acyclic graph (DAG) whose underlying undirected graph is planar admits an upward planar drawing. We are interested in pushing the notion of upward drawings beyond planarity by considering upward $k$-planar drawings of DAGs in which the
Patrizio Angelini +10 more
doaj +1 more source
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
openaire +2 more sources
Width, Depth, and Space: Tradeoffs between Branching and Dynamic Programming
Algorithms, 2018 Treedepth is a well-established width measure which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted than graphs of bounded tree- or pathwidth, we are interested in the algorithmic utility of this ...
Li-Hsuan Chen +3 more
doaj +1 more source
A General Reduction Theorem with Applications to Pathwidth and the Complexity of MAX 2-CSP [PDF]
, 2015 We prove a general reduction theorem which allows us to extend bounds for certain graph parameters on cubic graphs to bounds for general graphs taking into account the individual vertex degrees.
A Golovnev +18 more
core +3 more sources
Digraph Complexity Measures and Applications in Formal Language Theory [PDF]
, 2011 We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages.
Hermann Gruber +1 more
core +4 more sources
Packing independent cliques into planar graphs
Theory and Applications of GraphsThe indeque number of a graph is largest set of vertices that induce an independent set of cliques. We study the extremal value of this parameter for the class and subclasses of planar graphs, most notably for forests and graphs of pathwidth at most $2$.
Csaba Biró +2 more
doaj +1 more source
A simple linear-time algorithm for finding path-decompositions of small width [PDF]
, 1994 We described a simple algorithm running in linear time for each fixed constant $k$, that either establishes that the pathwidth of a graph $G$ is greater than $k$, or finds a path-decomposition of $G$ of width at most $O(2^{k})$.
Cattell, Kevin +2 more
core