Results 101 to 110 of about 307,259 (304)
The toroidal crossing number of K4,n
, 2009 In this paper, we show that the toroidal crossing number of K4,n, K1,3,n, K2,2,n, K1,1,2,n and K1,1,1,1,n is ⌊n4⌋[2n−4(1+⌊n4⌋)]. In addition, a new lower bound for the toroidal crossing number of Km,n has been obtained. We also discuss about the crossing
Ho, Pak Tung
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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
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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
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Tumour–host interactions in Drosophila: mechanisms in the tumour micro‐ and macroenvironment
Molecular Oncology, EarlyView.This review examines how tumour–host crosstalk takes place at multiple levels of biological organisation, from local cell competition and immune crosstalk to organism‐wide metabolic and physiological collapse. Here, we integrate findings from Drosophila melanogaster studies that reveal conserved mechanisms through which tumours hijack host systems to ...
José Teles‐Reis, Tor Erik Rusten
wiley +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
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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
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Molecular Oncology, EarlyView.Tumors contain diverse cellular states whose behavior is shaped by context‐dependent gene coordination. By comparing gene–gene relationships across biological contexts, we identify adaptive transcriptional modules that reorganize into distinct vulnerability axes.
Brian Nelson +9 more
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Crossing number is hard for cubic graphs
, 2006 It was proved by [M.R. Garey, D.S. Johnson, Crossing number is NP-complete, SIAM J. Algebraic Discrete Methods 4 (1983) 312–316] that computing the crossing number of a graph is an NP-hard problem.
Hliněný, Petr
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Counting and enumerating crossing-free geometric graphs
Journal of Computational Geometry, 2017 We describe a framework for constructing data structures which allow fast counting and enumeration of various types of crossing-free geometric graphs on a planar point set.
Manuel Wettstein
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Molecular Oncology, EarlyView.Pre‐analytical handling critically determines liquid biopsy performance. This study defines practical best‐practice conditions for cell‐free DNA (cfDNA) and extracellular vesicle–derived DNA (evDNA), showing how processing time, storage conditions, tube type, and plasma input volume affect DNA integrity and mutation detection.
Jonas Dohmen +11 more
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