Transducing paths in graph classes with unbounded shrubdepth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10515246" target="_blank" >RIV/00216208:11320/25:10515246 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0tkMQxgUSY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0tkMQxgUSY</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2022.103660" target="_blank" >10.1016/j.ejc.2022.103660</a>

Result language
angličtina
Original language name
Transducing paths in graph classes with unbounded shrubdepth
Original language description
Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is, has bounded shrubdepth) if, and only if, from C one cannot FO-transduce the class of all paths. This establishes one of the three remaining open questions posed by Blumensath and Courcelle about the MSO-transduction quasi-order, even in the stronger form that concerns FO-transductions instead of MSO-transductions. The backbone of our proof is a graph-theoretic statement that says the following: If a graph G excludes a path, the bipartite complement of a path, and a half-graph as semi-induced subgraphs, then the vertex set of G can be partitioned into a bounded number of parts so that every part induces a cograph of bounded height, and every pair of parts semi-induce a bi-cograph of bounded height. This statement may be of independent interest; for instance, it implies that the graphs in question form a class that is linearly χ-bounded.
Czech name
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Czech description
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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)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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