Degree of h-polynomials of edge ideals
Jennifer Biermann, Selvi Kara, Augustine O’Keefe, Joseph Skelton, Gabriel Sosa Castillo
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Source: Crossref
Published: Jul 8, 2025
DOI: 10.1007/s10801-025-01411-9
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Abstract In this paper, we investigate the degree of h -polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the h -polynomial for various fundamental classes of graphs such as paths, cycles, and bipartite graphs. To the best of our knowledge, this study represents the first investigation into the combinatorial interpretation of this algebraic invariant. Additionally, we characterize all connected graphs in which the sum of the Castelnuovo–Mumford regularity and the degree of the h -polynomial of an edge ideal achieve its maximum value, equal to the number of vertices in the graph.
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