Threshold-Coloring and Unit-Cube Contact Representation of Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190761" target="_blank" >RIV/00216208:11320/13:10190761 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-45043-3_4" target="_blank" >http://dx.doi.org/10.1007/978-3-642-45043-3_4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-45043-3_4" target="_blank" >10.1007/978-3-642-45043-3_4</a>

Result language
angličtina
Original language name
Threshold-Coloring and Unit-Cube Contact Representation of Graphs
Original language description
We study threshold coloring of graphs where the vertex colors, repre- sented by integers, describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is present and pairs of vertices with far colors imply the edge is absent. Not all planar graphs are threshold-colorable, but several subclasses, such as trees, some planar grids, and planar graphs with no short cycles can always be threshold-colored. Using these results we obtain unit-cube contact representation of several subclasses of planar graphs. We show the NP-completeness for two variants of the threshold coloring problem and describe a polynomial-time algorithm for another.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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