Results 51 to 60 of about 1,033 (146)

Packing independent cliques into planar graphs

Theory and Applications of Graphs
The 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 , Gabriel Collado, Oscar Zamora   +2 more
doaj   +1 more source

On edge-intersection graphs of k-bend paths in grids [PDF]

Discrete Mathematics & Theoretical Computer Science, 2010
Edge-intersection graphs of paths in grids are graphs that can be represented such that vertices are paths in a grid and edges between vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications
Therese Biedl, Michal Stern
doaj   +1 more source

Fractional List Packing for Layered Graphs

Journal of Graph Theory, Volume 113, Issue 1, Page 19-37, September 2026.
ABSTRACT The fractional list packing number χ ℓ • ( G ) of a graph G is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N need to be to ensure the existence of a “perfectly balanced” probability distribution on proper L‐colourings, that is, such ...
Stijn Cambie, Wouter Cames van Batenburg
wiley   +1 more source

Order-preserving Drawings of Trees with Approximately Optimal Height (and Small Width)

Journal of Graph Algorithms and Applications, 2020
In this paper, we study how to draw trees so that they are planar, straight-line and respect a given order of edges around each node. We focus on minimizing the height, and show that we can always achieve a height of at most $2pw(T)+1$, where $pw(T ...
Johannes Batzill, Therese Biedl
doaj   +1 more source

An Improved Quasi‐Isometry Between Graphs of Bounded Cliquewidth and Graphs of Bounded Treewidth

Journal of Graph Theory, Volume 112, Issue 4, Page 409-420, August 2026.
ABSTRACT Cliquewidth is a dense analogue of treewidth. It can be deduced from recent results by Hickingbotham [arXiv:2501.10840] and Nguyen, Scott, and Seymour [arXiv:2501.09839] that graphs of bounded cliquewidth are quasi‐isometric to graphs of bounded treewidth. We improve on this by showing that graphs of cliquewidth k admit a partition with ‘local,
Marc Distel
wiley   +1 more source

Semantic Tree-Width and Path-Width of Conjunctive Regular Path Queries [PDF]

Logical Methods in Computer Science
We show that the problem of whether a query is equivalent to a query of tree-width $k$ is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs).
Diego Figueira, Rémi Morvan
doaj   +1 more source

Parameterized Complexity of Safe Set

Journal of Graph Algorithms and Applications, 2020
In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e., a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the problem from
Rémy Belmonte, Tesshu Hanaka, Ioannis Katsikarelis, Michael Lampis, Hirotaka Ono, Yota Otachi   +5 more
doaj   +1 more source

Structural properties of graph products

Journal of Graph Theory, Volume 109, Issue 2, Page 107-136, June 2025.
Abstract Dujmovć, Joret, Micek, Morin, Ueckerdt, and Wood established that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path. Motivated by this result, this paper systematically studies various structural properties of cartesian, direct and strong products.
Robert Hickingbotham, David R. Wood
wiley   +1 more source

A Brief Overview of Applications of Tree-Width and Other Graph Width Parameters

Applied Mathematics on Science and Engineering
Graph theory, a fundamental branch of mathematics, centers on the study of networks composed of vertices (nodes) and edges, examining their paths, structures, and properties.
Takaaki Fujita
doaj   +1 more source

Parameterized Complexity of 1-Planarity

Journal of Graph Algorithms and Applications, 2018
We consider the problem of drawing graphs with at most one crossing per edge. These drawings, and the graphs that can be drawn in this way, are called $1$-planar.
Michael Bannister, Sergio Cabello, David Eppstein   +2 more
doaj   +1 more source