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

2024/05/10 by A. V. Jayanthan, S. A. Seyed Fakhari, Jayanthan, A. V. +5
Computer Science · Mathematics · #05E40 #13F55 #Advanced Graph Theory Research #Commutative Algebra (math.AC) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2405.06781

openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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