论文标题
公制图理论的一阶逻辑公理化
First-order logic axiomatization of metric graph theory
论文作者
论文摘要
本注意事项的主要目的是提供一阶逻辑，并在度量图理论中进行介入（fOLB）公理（fOLB）公理化，类似于塔斯基（Tarski）的欧几里得几何形状的公理化。 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,二分pasch和Peano图，细胞和高细胞部分立方体，几乎是米迪安图，类似网状的部分立方体）和Gromov双曲线图。另一方面，我们表明某些类别的图（包括弦，平面，欧拉和拆卸图）与公表示图理论密切相关，但以组合或拓扑的方式定义，不允许这样的体积化。
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.
