In the origins of complexity theory Booth and Lueker showed that the question of whether two graphs are isomorphic or not can be reduced to the special case of chordal graphs. To prove that, they defined a transformation from graphs G to chordal graphs BL(G). The projective resolutions of the associated edge ideals is manageable and we investigate to what extent their Betti tables also tell non-isomorphic graphs apart. It turns out that the coefficients describing the decompositions of Betti tables into pure diagrams in Boij-Soderberg theory are much more explicit than the Betti tables themselves, and they are expressed in terms of classical statistics of the graph G.

中文翻译：

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图同构化简的显式 Boij-Söderberg 理想理论

在复杂性理论的起源中，Booth 和 Lueker 表明，两个图是否同构的问题可以简化为弦图的特殊情况。为了证明这一点，他们定义了从图 G 到弦图 BL(G) 的转换。相关边理想的投影分辨率是可管理的，我们调查了他们的 Betti 表在多大程度上也区分了非同构图。事实证明，在 Boij-Soderberg 理论中描述 Betti 表分解为纯图的系数比 Betti 表本身要明确得多，它们用图 G 的经典统计量表示。