Results 111 to 120 of about 308,302 (304)
Note on k-planar crossing numbers [PDF]
, 2018 The crossing number CR(G) of a graph G = (V, E) is the smallest number of edge crossings over all drawings of G in the plane. For any k >= 1, the k-planar crossing number of G, CRk(G), is defined as the minimum of CR(G(0)) + CR(G(1)) + ...
Toth, Csaba D. +7 more
core +1 more source
On the 2-Colored Crossing Number
, 2019 Let $D$ be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of $D$ is the minimum number of crossings between edges of the same color, taken over all possible 2-colorings of the edges of $D$. First, we show lower and upper bounds on the rectilinear 2-colored crossing number for the complete graph $K_n$.
Oswin Aichholzer +6 more
openaire +2 more sources
Discrete Applied Mathematics, 2007 The \(k\)-planar crossing number of a graph \(G\), denoted by \(\text{cr}_k(G)\), is the minimum number of crossings of its edges over all possible drawings of the \(G\) in \(k\) planes. This parameter is related to the thickness parameter: \(\text{cr}_k(G)= 0\) if and only if \(G\) has thickness at most \(k\).
Farhad Shahrokhi +3 more
openaire +2 more sources
Diversity and complexity in neural organoids
FEBS Letters, EarlyView.Neural organoid research aims to expand genetic diversity on one side and increase tissue complexity on the other. Chimeroids integrate multiple donor genomes within single organoids. Self‐organising multi‐identity organoids, exogenous cell seeding, or enforced assembly of region‐specific organoids contribute to tissue complexity.
Ilaria Chiaradia, Madeline A. Lancaster
wiley +1 more source
Crossing number of graphs with rotation systems [PDF]
, 2007 We show that computing the crossing number of a graph with a given rotation system is NP-complete. This result leads to a new and much simpler proof of Hliněn´y’s result, that computing the crossing number of a cubic graph (without rotation system) is NP-
Daniel Stefankovič +5 more
core +1 more source
From the Crossing Numbers of K5 + Pn and K5 + Cn to the Crossing Numbers of Wm + Sn and Wm + Wn
AxiomsThe crossing number of a graph is a significant measure that indicates the complexity of the graph and the difficulty of visualizing it. In this paper, we examine the crossing numbers of join products involving the complete graph K5 with discrete graphs,
Michal Staš +2 more
doaj +1 more source
Review of researches on seismic response of close underground crossing structures
Yantu gongcheng xuebao, 2019 In view of the design and use requirements, a large number of close underground crossing projects have emerged, forming a complex interaction system between soil-crossing structural groups. When a number of underground structures are close to each other,
WANG Guo-bo 1,2, PENG Xiang-jun 1, HAO Peng-fei 1, WEI Hao-hao 1
doaj +1 more source
FEBS Letters, EarlyView.Plasma membranes contain dynamic nanoscale domains that organize lipids and receptors. Because viruses operate at similar scales, this architecture shapes early infection steps, including attachment, receptor engagement, and entry. Using influenza A virus and HIV‐1 as examples, we highlight how receptor nanoclusters, multivalent glycan interactions ...
Jan Schlegel, Christian Sieben
wiley +1 more source
Infinite families of crossing-critical graphs with a given crossing number [PDF]
, 1984 A graph is crossing-critical if deleting any edge decreases its crossing number on the plane. It is proved that, for any n ⩾ 3, there is an infinite family of 3-connected crossing-critical graphs with crossing number ...
Širáň, Jozef, Jozef Širáň
core +1 more source
FEBS Letters, EarlyView.Ascidian Ciona larvae initially show strong clockwise tail twisting, which is largely corrected during development. However, a small residual twist remains. This study shows that organized helical myofibrils in tail muscles mechanically stabilize this residual asymmetry, preventing complete restoration of bilateral symmetry and revealing how embryos ...
Yuki S. Kogure +3 more
wiley +1 more source