First-order logic axiomatization of metric graph theory

The main goal of this note is to provide a First-Order Logic with Betweenness (FOLB) axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to Tarski's axiomatization of Euclidean geometry. We provide such an axiomatization for weakly modular graphs and their...

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Vydáno v:Theoretical computer science Ročník 993; s. 114460
Hlavní autoři: Chalopin, Jérémie, Changat, Manoj, Chepoi, Victor, Jacob, Jeny
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 27.04.2024
Elsevier
Témata:
[formula omitted] games
Axiomatization
Betweenness
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
First-order logic
Mathematics
Metric Geometry
Metric graph theory
Betweenness
First-order logic
Axiomatization
Metric graph theory
E−F games
ISSN:0304-3975, 1879-2294
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Shrnutí:The main goal of this note is to provide a First-Order Logic with Betweenness (FOLB) axiomatization of the main classes of graphs occurring in Metric Graph Theory, in analogy to Tarski's axiomatization of Euclidean geometry. We provide such an axiomatization for weakly modular graphs and their principal subclasses (median and modular graphs, bridged graphs, Helly graphs, dual polar graphs, etc), basis graphs of matroids and even Δ-matroids, partial cubes and their subclasses (ample partial cubes, tope graphs of oriented matroids and complexes of oriented matroids, bipartite Pasch and Peano graphs, cellular and hypercellular partial cubes, almost-median graphs, netlike partial cubes), and Gromov hyperbolic graphs. On the other hand, we show that some classes of graphs (including chordal, planar, Eulerian, and dismantlable graphs), closely related with Metric Graph Theory, but defined in a combinatorial or topological way, do not allow such an axiomatization.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114460