Bisimplicial separators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493537" target="_blank" >RIV/00216208:11320/24:10493537 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gzI4DpW42T" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gzI4DpW42T</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.23098" target="_blank" >10.1002/jgt.23098</a>
Alternative languages
Result language
angličtina
Original language name
Bisimplicial separators
Original language description
A minimal separator of a graph G is a set S subset of V (G) such that there exist vertices a, b is an element of V (G)S with the property that S separates a from b in G, but no proper subset of S does. For an integer k >= 0, we say that a minimal separator is k-simplicial if it can be covered by k cliques and denote by G(k) the class of all graphs in which each minimal separator is k-simplicial. We show that for each k >= 0, the class G(k) is closed under induced minors, and we use this to show that the MAXIMUM WEIGHT STABLE SET problem can be solved in polynomial time for G(k). We also give a complete list of minimal forbidden induced minors for G(2). Next, we show that, for k >= 1, every nonnull graph in G(k) has a k-simplicial vertex, that is, a vertex whose neighborhood is a union of k cliques; we deduce that the MAXIMUM WEIGHT CLIQUE problem can be solved in polynomial time for graphs in G(2). Further, we show that, for k >= 3, it is NP-hard to recognize graphs in G(k); the time complexity of recognizing graphs in G(2) 2 is unknown. We also show that the MAXIMUM CLIQUE problem is NP-hard for graphs in G(3). Finally, we prove a decomposition theorem for diamond-free graphs in G(2) (where the diamond is the graph obtained from K-4 by deleting one edge), and we use this theorem to obtain polynomial-time algorithms for the VERTEX COLORING and recognition problems for diamond-free graphs in G(2), and improved running times for the MAXIMUM WEIGHT CLIQUE and MAXIMUM WEIGHT STABLE SET problems for this class of graphs.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Graph Theory
ISSN
0364-9024
e-ISSN
1097-0118
Volume of the periodical
106
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
816-842
UT code for WoS article
001200260900001
EID of the result in the Scopus database
2-s2.0-85190460672