What does this research mean for the field?

For all bipartite graphs, the induced matching number equals the ordered matching number. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to characterize bipartite graphs where the induced matching number equals the ordered matching number.

March 5, 2026Open Access

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

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. (Tue,) studied this question.

synapsesocial.com/papers/69a91de0d6127c7a504c11cc https://doi.org/https://doi.org/10.5802/alco.461

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