Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10451828" target="_blank" >RIV/00216208:11320/22:10451828 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-031-20624-5_31" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-031-20624-5_31</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-20624-5_31" target="_blank" >10.1007/978-3-031-20624-5_31</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs

Popis výsledku v původním jazyce

The CSP dichotomy conjecture has been recently established, but a number of other dichotomy questions remain open, including the dichotomy classification of list homomorphism problems for signed graphs. Signed graphs arise naturally in many contexts, including for instance nowhere-zero flows for graphs embedded in non-orientable surfaces. For a fixed signed graph ????^H^, the list homomorphism problem asks whether an input signed graph ????^G^ with lists ????(????)SUBSET OF OR EQUAL TO  ????(????^),????ELEMENT OF????(????^),L(v)SUBSET OF OR EQUAL TOV(H^),vELEMENT OFV(G^), admits a homomorphism f to ????^H^ with all ????(????)ELEMENT OF????(????),????ELEMENT OF????(????^)f(v)ELEMENT OFL(v),vELEMENT OFV(G^).Usually, a dichotomy classification is easier to obtain for list homomorphisms than for homomorphisms, but in the context of signed graphs a structural classification of the complexity of list homomorphism problems has not even been conjectured, even though the classification of the complexity of homomorphism problems is known.Kim and Siggers have conjectured a structural classification in the special case of &quot;weakly balanced&quot; signed graphs. We confirm their conjecture for reflexive and irreflexive signed graphs; this generalizes previous results on weakly balanced signed trees, and weakly balanced separable signed graphs [1,2,3]. In the reflexive case, the result was first presented in [19], where the proof relies on a result in this paper. The irreflexive result is new, and its proof depends on first deriving a theorem on extensions of min orderings of (unsigned) bipartite graphs, which is interesting on its own.

Název v anglickém jazyce

Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs

Popis výsledku anglicky

The CSP dichotomy conjecture has been recently established, but a number of other dichotomy questions remain open, including the dichotomy classification of list homomorphism problems for signed graphs. Signed graphs arise naturally in many contexts, including for instance nowhere-zero flows for graphs embedded in non-orientable surfaces. For a fixed signed graph ????^H^, the list homomorphism problem asks whether an input signed graph ????^G^ with lists ????(????)SUBSET OF OR EQUAL TO  ????(????^),????ELEMENT OF????(????^),L(v)SUBSET OF OR EQUAL TOV(H^),vELEMENT OFV(G^), admits a homomorphism f to ????^H^ with all ????(????)ELEMENT OF????(????),????ELEMENT OF????(????^)f(v)ELEMENT OFL(v),vELEMENT OFV(G^).Usually, a dichotomy classification is easier to obtain for list homomorphisms than for homomorphisms, but in the context of signed graphs a structural classification of the complexity of list homomorphism problems has not even been conjectured, even though the classification of the complexity of homomorphism problems is known.Kim and Siggers have conjectured a structural classification in the special case of &quot;weakly balanced&quot; signed graphs. We confirm their conjecture for reflexive and irreflexive signed graphs; this generalizes previous results on weakly balanced signed trees, and weakly balanced separable signed graphs [1,2,3]. In the reflexive case, the result was first presented in [19], where the proof relies on a result in this paper. The irreflexive result is new, and its proof depends on first deriving a theorem on extensions of min orderings of (unsigned) bipartite graphs, which is interesting on its own.

Druh

D - Stať ve sborníku

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

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

Lecture Notes in Computer Science, vol 13568

ISBN

978-3-031-20623-8

ISSN

—

e-ISSN

—

Počet stran výsledku

17

Strana od-do

510-526

Název nakladatele

Springer

Místo vydání

Berlin

Místo konání akce

Guanajuato, Mexico

Datum konání akce

7. 11. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—