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Furthermore, the reduced molecule gets a complete planar structure (Fig. 2) according to the optimized geometry.
Meshedness is meant to describe whether a network has a tree-like structure (meshedness = 0) or is a complete planar graph (meshedness = 1) regardless of how dense the veins are packed.
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Crucial HMBC correlation from the anomeric H-1′ to the quaternary C-8 carbon (δC 79.4) connected substructure D to the sugar unit to complete the planar structure of the glycoside.
In the present paper, we prove that the edge total domination problem is NP-complete for planar graphs with maximum degree three, and for undirected path graphs, a subclass of chordal graphs and a superclass of trees.
Let G be a planar complete bipartite graph of order n.
We classify all integer numbers n for which ({mathbb {G}}({{mathbb {Z}}}_n)) is a complete or a planar graph.
We show that this problem is NP-complete, even in planar bipartite graphs.
We prove that the F3-domination problem is NP-complete for bipartite planar graphs and for chordal graphs.
Many NP-complete problems on planar graphs are "fixed-parameter tractable:" Recent theoretical work provided tree decomposition-based fixed-parameter algorithms exactly solving various parameterized problems on planar graphs, among others VERTEX COVER, in time O(c√kn).
At a meter to sub-meter scale, we completed the 2D planar data with vertical measures - like the height of the scarp - that we measured using a handheld laser range finder (LaserAce 300).
Our results allow one to extend the understanding of the dynamical repertoire hosted in this unfolding, by giving a complete description of the planar bursting activity that can be obtained thanks to a coupling of the planar unfolding with a slower system.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com