Betti numbers of normal edge rings (II)
Abstract
We compute the Betti numbers of the edge rings of multi-path graphs using the induced-subgraph approach introduced in WL1. Here, a multi-path graph refers to a simple graph composed of several paths that have the same starting point and the same ending point. Special cases include the graph Gr,d introduced in GHK, the graph Gr,s,d introduced in NN, and the graph B,h introduced in LZ. In particular, we show that all the multi-graded Betti numbers of a multi-path graph are the top multi-graded Betti numbers of some of its induced subgraphs.
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