Column Planarity and Partially-Simultaneous Geometric Embedding

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00483679" target="_blank" >RIV/67985807:_____/17:00483679 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.7155/jgaa.00446" target="_blank" >http://dx.doi.org/10.7155/jgaa.00446</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7155/jgaa.00446" target="_blank" >10.7155/jgaa.00446</a>

Result language

angličtina

Original language name

Column Planarity and Partially-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 the maximum size of column planar subsets of trees: every 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. In addition, we show that every outerplanar graph has a column planar set of size at least n/2. We also consider a relaxation of simultaneous geometric embedding (SGE), which we call partially-simultaneous geometric embedding (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, which are PSGEs in which at least k vertices are mapped to the same point for both graphs. In particular, we show that every two trees on n vertices admit an 11n/17-PSGE and every two outerplanar graphs admit an n/4-PSGE.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Graph Algorithms and Applications

ISSN

1526-1719

e-ISSN

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Volume of the periodical

21

Issue of the periodical within the volume

6

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

983-1002

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85037335542