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March 5, 2026Algebraic Combinatorics0 citationsOpen Access

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

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AJA. V. JayanthanSFS. A. Seyed FakhariISIrena Swanson

Key Points

  • This research aims to characterize bipartite graphs where the induced matching number equals the ordered matching number.
  • Characterization of bipartite graphs based on matching numbers.
  • Analysis of induced and ordered matching definitions.
  • Establishment of Castelnuovo-Mumford regularity for edge ideals.
  • Identified conditions under which the induced and ordered matching numbers are equal.
  • Established relationships between edge ideals and depth for powers of cover ideals.

Abstract

Let G be a finite simple graph and let ind-match ( G ) and ord-match ( G ) denote the induced matching number and the ordered matching number of G , respectively. We characterize all bipartite graphs G with ind-match ( G ) = ord-match ( G ) . We establish the Castelnuovo-Mumford regularity of powers of edge ideals and depth of powers of cover ideals for such graphs.

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Cite This Study

Jayanthan et al. (2026) studied this question.

synapsesocial.com/papers/69a91de0d6127c7a504c11cchttps://doi.org/10.5802/alco.461
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