Sesión Matemática DiscretaAbout the determinant of graph with perfect matching
Diego G. Martinez
Universidad Nacional de San Luis - IMASL -CONICET, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
In 2022, Jaume and Molina introduced the FP-KE decomposition, see [1]. This is a structural decomposition of graphs in terms of flowers and posies. Flowers were introduced by Edmonds (1965) in the context of matching theory. Posies were introduced by Sterboul (1979) to characterize K\H{o}nig-Egerv\'{a}ry graphs.
The FP-KE Decomposition of a graph breaks the graph into two disjoint subgraphs, one of which may be empty. It always yields a K\H{o}nig-Egerv\'{a}ry subgraph, named the KE-part of the graph, and an FP-part, which is a subgraph where every vertex is in a flower or in a posy.
We show that the FP-KE Decomposition of graphs with perfect matchings is multiplicative with respect to the determinant: $\det(G) = \det(\text{FP}(G) \cdot \text{KE}(G))$.
Trabajo en conjunto con: Daniel A. Jaume (Universidad Nacional de San Luis - IMASL - CONICET) y Cristian Panelo (Universidad Nacional de San Luis).
Referencias
[1] D. Jaume and G. Molina, A new graph decomposition: the FP-KE Decomposition, submitted.