Results 71 to 80 of about 200,785 (277)
The Weisfeiler-Leman Dimension of Planar Graphs is at most 3
, 2017 We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables.
Kiefer, Sandra +2 more
core +1 more source
Harnessing Fungal Biowelding for Constructing Mycelium‐Engineered Materials
Advanced Engineering Materials, EarlyView.Mycelium‐bound composites (MBCs) offer low‐carbon alternatives for construction, yet interfacial bonding remains a critical challenge. This review examines fungal biowelding as a biocompatible adhesive, elucidating mycelium‐mediated interfacial mechanisms and their role in material assembly. Strategies to optimize biowelding are discussed, highlighting
Xue Brenda Bai +2 more
wiley +1 more source
Fast simulation of planar Clifford circuits [PDF]
QuantumA general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more generally ...
David Gosset +3 more
doaj +1 more source
Mixed Linear Layouts of Planar Graphs
, 2017 A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured
C Bachmaier +12 more
core +1 more source
A Workflow to Accelerate Microstructure‐Sensitive Fatigue Life Predictions
Advanced Engineering Materials, EarlyView.This study introduces a workflow to accelerate predictions of microstructure‐sensitive fatigue life. Results from frameworks with varying levels of simplification are benchmarked against published reference results. The analysis reveals a trade‐off between accuracy and model complexity, offering researchers a practical guide for selecting the optimal ...
Luca Loiodice +2 more
wiley +1 more source
Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs
Discussiones Mathematicae Graph Theory, 2020 Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings
Song Wen-Yao +2 more
doaj +1 more source
Advanced Engineering Materials, EarlyView.Carbon nanomaterial‐reinforced epoxy composites exhibit pronounced piezoresistive behavior, enabling intrinsic damage sensing under cyclic and fatigue loading. This review critically compares carbon nanotube and graphene systems, correlating filler content, percolation threshold, and gauge factor with sensing stability and damage evolution.
J. M. Parente +3 more
wiley +1 more source
On the Synthesis of Planar Graphs with Given Properties
Кібернетика та комп'ютерні технологіїThe problem of studying the structural properties of planar subgraphs G\v, where v is an arbitrary vertex of a graph G of undirected genus, is considered, using cell chains that connect limit cycles with points of a given set M of the graph G\v.
Volodymyr Petrenjuk, Dmytro Petreniuk
doaj +1 more source
Regularity and Planarity of Token Graphs
Discussiones Mathematicae Graph Theory, 2017 Let G = (V, E) be a graph of order n and let 1 ≤ k < n be an integer. The k-token graph of G is the graph whose vertices are all the k-subsets of V, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G.
Carballosa Walter +3 more
doaj +1 more source
$1$-string $B_2$-VPG representation of planar graphs
Journal of Computational Geometry, 2016 In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation—a string representation using paths in a rectangular grid that contain at most two bends.
Therese Biedl, Martin Derka
doaj +1 more source