Results 251 to 260 of about 22,383 (289)
Real-time NIR-II fluorescence imaging-guided precision thrombolysis with a molecularly planarized phototheranostic agent. [PDF]
Chem SciZhang G, Si L, Zhou F, Song X, Wang H.
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Synchronized Planarity with Applications to Constrained Planarity Problems [PDF]
ACM Transactions on Algorithms, 2023 We introduce the problem S ynchronized P lanarity . Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. S ynchronized P
Simon Dominik Fink +2 more
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Beyond level planarity: Cyclic, torus, and simultaneous level planarity
Theoretical Computer Science, 2020 In this paper we settle the computational complexity of two open problems related to the extension of the notion of level planarity to surfaces different from the plane. Namely, we show that the problems of testing the existence of a level embedding of a
Fabrizio Frati +2 more
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Strip Planarity Testing for Embedded Planar Graphs [PDF]
Algorithmica, 2016 In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $γ:V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each edge is monotone in the $y$-direction and, for any $u,v\in V$ with $γ(u)
Fabrizio Frati +2 more
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SIAM Journal on Discrete Mathematics, 1994
A separator in a graph \(G\) is a partition \((A,B,C)\) of \(V(G)\) such that \(| A|\), \(| B|\leq {2\over 3}| V(G)|\) and no vertex in \(A\) is adjacent to any vertex in \(B\); its order is \(| C|\). The authors give a short proof of a theorem of Lipton and Tarjan that for any planar graph with \(n\) vertices there is a separator of order \(\leq 2 ...
Noga Alon +2 more
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A separator in a graph \(G\) is a partition \((A,B,C)\) of \(V(G)\) such that \(| A|\), \(| B|\leq {2\over 3}| V(G)|\) and no vertex in \(A\) is adjacent to any vertex in \(B\); its order is \(| C|\). The authors give a short proof of a theorem of Lipton and Tarjan that for any planar graph with \(n\) vertices there is a separator of order \(\leq 2 ...
Noga Alon +2 more
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HV-planarity: Algorithms and complexity
Journal of Computer and System Sciences, 2019 An HV-graph is a planar graph with vertex-degree at most four such that each edge is labeled either H (horizontal) or V (vertical). The HV-planarity testing problem asks whether an HV-graph admits an HV-drawing, that is, a planar drawing such that each ...
Maurizio Patrignani +2 more
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Fan-planarity: Properties and complexity [PDF]
Theoretical Computer Science, 2015 In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. Fan-planar drawings have been recently introduced by Kaufmann and Ueckerdt [35], who proved that every n-vertex fan-planar drawing has at most 5. n-.
Maurizio Patrignani +2 more
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IEEE Transactions on Computers, 1981
Summary: Those bases which permit the realization of a planar crossover are characterized.
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Summary: Those bases which permit the realization of a planar crossover are characterized.
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Planar and non-planar borepins
Molecular Physics, 1996Theoretical studies of borepin and its B-substituted derivatives show planar structures with weak out-of-plane bending modes, often leading to boat-shaped borepins. The lowest vibrational frequency of borepin is 167 cm-1 at both HF/6-31G* and MP2/6-31G* levels, compared to 248 cm-1 calculated for the isoelectronic tropylium ion.
JEROME SCHULMAN, RAYMOND DISCH
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Journal of Knot Theory and Its Ramifications, 2002
Let S be a connected open subset of 2-sphere S2 which is identified with the extended plane R2 ∪ {∞}. We assume that S contains the n segments {1, 2, …, n} × [-1, 1]. An n-lace ℓ (in S) is the union ℓ1 ∪ … ∪ ℓn of disjoint simple arcs in S such that ∂ ℓi = {(i, 1), (π (i),-1)}, i = 1, …, n, for some permutation π of {1, 2, …, n}.
Jin, GT Jin, Gyo Taek, Kim, H
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Let S be a connected open subset of 2-sphere S2 which is identified with the extended plane R2 ∪ {∞}. We assume that S contains the n segments {1, 2, …, n} × [-1, 1]. An n-lace ℓ (in S) is the union ℓ1 ∪ … ∪ ℓn of disjoint simple arcs in S such that ∂ ℓi = {(i, 1), (π (i),-1)}, i = 1, …, n, for some permutation π of {1, 2, …, n}.
Jin, GT Jin, Gyo Taek, Kim, H
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