Results 111 to 120 of about 59,909 (247)

Tight Bounds for Hypercube Minor‐Universality

Journal of Graph Theory, EarlyView.
ABSTRACT A graph G $G$ is m $m$‐minor‐universal if every graph H $H$ with at most m $m$ edges and no isolated vertices is contained as a minor in G $G$. Recently, Benjamini, Kalifa and Tzalik proved that there is an absolute constant c>0 $c\gt 0$ such that the d $d$‐dimensional hypercube Qd ${Q}_{d}$ is (c⋅2d/d $c\cdot {2}^{d}/d$)‐minor‐universal ...
Emma Hogan, Lukas Michel, Alex Scott, Youri Tamitegama, Jane Tan, Dmitry Tsarev   +5 more
wiley   +1 more source

Motion planning in cartesian product graphs

Discussiones Mathematicae Graph Theory, 2014
Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole.
Deb Biswajit, Kapoor Kalpesh
doaj   +1 more source

Signed Projective Cubes, a Homomorphism Point of View

Journal of Graph Theory, EarlyView.
ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen, Reza Naserasr, Alessandra Sarti   +2 more
wiley   +1 more source

Fractional List Packing for Layered Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ 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 $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley   +1 more source

A note on a Vizing's generalized conjecture [PDF]

Opuscula Mathematica, 2007
In this note we give a generalized version of Vizing's conjecture concerning the distance domination number for the cartesian product of two graphs.
Mostafa Blidia, Mustapha Chellali
doaj  

MRI for Lung Cancer Management: Any Closer to Clinical Application?

Journal of Magnetic Resonance Imaging, EarlyView.
ABSTRACT Management of lung cancer (LC) encompasses screening, diagnosis, staging, radiotherapy planning and guidance, therapy monitoring and surveillance. Across these domains, magnetic resonance imaging (MRI) offers a range of morphological and functional imaging capabilities—including diffusion‐weighted imaging (DWI), dynamic contrast‐enhanced (DCE)
Juergen Biederer, Liisa L. Bergmann, Jeanne B. Ackman, Bruno Hochhegger, Lea Azour, Simon M. F. Triphan, Julien Dinkel, Yoshiharu Ohno, Yoshiyuki Ozawa, Edwin J. R. van Beek, Lena Wucherpfennig   +10 more
wiley   +1 more source

Hamiltonicity of Cartesian products of graphs

A path factor in a graph $G$ is a factor of $G$ in which every component is a path on at least two vertices. Let $T\Box P_n$ be the Cartesian product of a tree $T$ and a path on $n$ vertices. Kao and Weng proved that $T\Box P_n$ is hamiltonian if $T$ has a path factor, $n$ is an even integer and $n\geq 4Δ(T)-2$. They conjectured that for every $Δ\geq 3$
Ladinek, Irena Hrastnik, Vukićević, Žana Kovijanić, Erker, Tjaša Paj, Špacapan, Simon   +3 more
openaire   +2 more sources

Free‐Breathing 3D Whole Heart and Aorta Cine MRI Without Contrast Agent—Comparison to Clinical Standard

Journal of Magnetic Resonance Imaging, EarlyView.
ABSTRACT Background The demand for cardiac MRI is increasing with the growing burden of cardiovascular disease. However, conventional protocols require sequential acquisitions for multi‐breath‐hold 2D cine and 3D MR angiography (MRA), which is time‐consuming.
Ruixin Chen, Huangling Lu, Alexandru Cernicanu, Jos Westenberg, Merlijn Sevenster, Jochen Keupp, Jakob Meineke, Hildo J. Lamb   +7 more
wiley   +1 more source

Explicit Formulas for the Complexity of Networks Produced by New Duplicating Corona and Cartesian Product

Journal of Mathematics
One important algebraic invariant in networks is complexity. This invariant ensures the accuracy and dependability of the network. In this paper, we employ a combinatorial approach to determine the graph’s complexity. A fundamental set of building blocks
Mohamed R. Zeen El Deen, Walaa A. Aboamer, Hamed M. El-Sherbiny   +2 more
doaj   +1 more source

Cuts in Cartesian Products of Graphs

, 2011
The k-fold Cartesian product of a graph G is defined as a graph on k-tuples of vertices, where two tuples are connected if they form an edge in one of the positions and are equal in the rest. Starting with G as a single edge gives G^k as a k-dimensional hypercube.
Sachdeva, Sushant, Tulsiani, Madhur
openaire   +2 more sources