Bisimplicial separators

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Bisimplicial separators

Popis výsledku v původním jazyce

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 &gt;= 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 &gt;= 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 &gt;= 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 &gt;= 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.

Název v anglickém jazyce

Bisimplicial separators

Popis výsledku anglicky

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 &gt;= 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 &gt;= 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 &gt;= 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 &gt;= 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal of Graph Theory

ISSN

0364-9024

e-ISSN

1097-0118

Svazek periodika

106

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

816-842

Kód UT WoS článku

001200260900001

EID výsledku v databázi Scopus

2-s2.0-85190460672