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arXiv · 2405.06781

Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs

A. V. Jayanthan·S. A. Seyed Fakhari·I. Swanson·S. Yassemi
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Abstract

Let G be a finite simple graph and let indm(G) and ordm(G) denote the induced matching number and the ordered matching number of G, respectively. We characterize all bipartite graphs G with indm(G) = ordm(G). We establish the Castelnuovo-Mumford regularity of powers of edge ideals and depth of powers of cover ideals for such graphs. We also give formulas for the count of connected non-isomorphic spanning subgraphs of the complete bipartite graph K_{m,n} for which indm(G) = ordm(G) = 2, with an explicit expression for the count when m = 2,3,4 and m <= n.

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A. V. Jayanthan, S. A. Seyed Fakhari, I. Swanson, S. Yassemi. 2024-05-10. Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs. https://arxiv.org/abs/2405.06781

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