2025/12/05 by Chau, Trung, Sheng, Richie, Tribone, Tim +1
#13D02 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.05376
The t-connected ideal of a graph G is generated by all connected induced subgraphs of G with t vertices. When t = 2, this coincides with the usual edge ideal of the graph. Following the work of Faridi et al., we give a classification of the graphs whose t-connected ideals are minimally resolved by their Scarf complex. We also consider the t-path ideal of a graph G which is the ideal generated by all paths of length t in G. In this case, we are able to give a classification of the same type for paths of length t = 4.