Column Planarity and Partial Simultaneous Geometric Embedding

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43923651" target="_blank" >RIV/49777513:23520/14:43923651 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007%2F978-3-662-45803-7_22" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-662-45803-7_22</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-662-45803-7_22" target="_blank" >10.1007/978-3-662-45803-7_22</a>

Result language
angličtina
Original language name
Column Planarity and Partial Simultaneous Geometric Embedding
Original language description
We introduce the notion of column planarity of a subset R of the vertices of a graph G. Informally, we say that R is column planar in G if we can assign x-coordinates to the vertices in R such that any assignment of y-coordinates to them produces a partial embedding that can be completed to a plane straight-line drawing of G. Column planarity is both a relaxation and a strengthening of unlabeled level planarity. We prove near tight bounds for column planar subsets of trees: any tree on n vertices contains a column planar set of size at least 14n/17 and for any epsilon > 0 and any sufficiently large n, there exists an n-vertex tree in which every column planar subset has size at most (5/6 + epsilon)n. We also consider a relaxation of simultaneous geometric embedding (SGE), which we call partial SGE (PSGE). A PSGE of two graphs G_1 and G_2 allows some of their vertices to map to two different points in the plane. We show how to use column planar subsets to construct k-PSGEs in which k ve
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: New excellence in human resources</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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