Results 21 to 30 of about 51 (49)

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

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

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

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, Felix Reidl, Peter Rossmanith, Fernando Sánchez Villaamil   +3 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

On tree decompositions whose trees are minors

Journal of Graph Theory, Volume 106, Issue 2, Page 296-306, June 2024.
Abstract In 2019, Dvořák asked whether every connected graph G $G$ has a tree decomposition ( T , B ) $(T,{\rm{ {\mathcal B} }})$ so that T $T$ is a subgraph of G $G$ and the width of ( T , B ) $(T,{\rm{ {\mathcal B} }})$ is bounded by a function of the treewidth of G $G$.
Pablo Blanco, Linda Cook, Meike Hatzel, Claire Hilaire, Freddie Illingworth, Rose McCarty   +5 more
wiley   +1 more source

The product structure of squaregraphs

Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.
Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham, Paul Jungeblut, Laura Merker, David R. Wood   +3 more
wiley   +1 more source

LSTM‐based deep learning framework for adaptive identifying eco‐driving on intelligent vehicle multivariate time‐series data

IET Intelligent Transport Systems, Volume 18, Issue 1, Page 186-202, January 2024.
In the context of automated driving, the connected and automated vehicles (CAVs) technology unlock the energy saving potential. This paper develops an LSTM‐based deep learning framework for eco‐driving adaptive identification on Intelligent vehicle multivariate time series data.
Lixin Yan, Le Jia, Shan Lu, Liqun Peng, Yi He   +4 more
wiley   +1 more source

The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations

Algorithms
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width
Frank Gurski, Robin Weishaupt
doaj   +1 more source

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Approximating Pathwidth for Graphs of Small Treewidth

ACM Transactions on Algorithms, 2023
Wojciech Nadara, Bartosz Walczak, Gwenael Joret   +2 more
exaly