Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913760437862400 |
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| author | Jayanthan, A. V. Fakhari, S. A. Seyed Swanson, I. Yassemi, S. |
| author_facet | Jayanthan, A. V. Fakhari, S. A. Seyed Swanson, I. Yassemi, S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs Jayanthan, A. V. Fakhari, S. A. Seyed Swanson, I. Yassemi, S. Commutative Algebra 13F55, 05E40 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. |
| title | Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs |
| topic | Commutative Algebra 13F55, 05E40 |
| url | https://arxiv.org/abs/2405.06781 |