Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

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)

Project

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Continuities

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

Publication year

2022

Confidentiality

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

Article name in the collection

Lecture Notes in Computer Science, vol 13568

ISBN

978-3-031-20623-8

ISSN

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e-ISSN

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Number of pages

17

Pages from-to

510-526

Publisher name

Springer

Place of publication

Berlin

Event location

Guanajuato, Mexico

Event date

Nov 7, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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