Sesión Matemática DiscretaA New Formula for the Determinant of a Graph
Daniel A. Jaume
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.
It is known that the vertices of any graph $G$ can be efficiently partitioned into two sets $X$, $\bar{X}$, where $G[X]$ is K\H{o}nig-Egerv\'ary, $G[\bar{X]}$ is $2$-bicritical, and $\alpha(G)=\alpha(G[X])+\alpha(G[\bar{X}])$, see [1] and [2]. It is shown here that $\det(G)=\det(G[X])\cdot \det(G[\bar{X}]).$
Trabajo en conjunto con: Craig Larson (Virginia Commonwealth University) y Gonzalo Molina (Universidad Nacional de San Luis).
Referencias
[1] C. E. Larson. A note on critical independence reductions. Bull. Inst. Combin. Appl., 51:34–46, 2007.
[2] C. E. Larson. The critical independence number and an independence decomposition. European J. Combin., 32(2):294–300, 2011