EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 92(106), pp. 43–51 (2012)

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COMPLEXES OF DIRECTED TREES OF COMPLETE MULTIPARTITE GRAPHS

Dusko Jojic

Department of Mathematics, University of Banja Luka, Banja Luka, Bosnia and Herzegovina

Abstract: For every directed graph $D$ we consider the complex of all directed subforests $\Delta(D)$. The investigation of these complexes was started by D. Kozlov. We generalize a result of Kozlov and prove that complexes of directed trees of complete multipartite graphs are shellable. We determine the $h$-vector of $\Delta(\overrightarrow{K}_{m,n})$ and the homotopy type of $\Delta(\overrightarrow{K}_{n_1,n_2,\ldots,n_k})$.

Keywords: shellability; directed trees; multipartite graph

Classification (MSC2000): 52B22; 05C20

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Electronic fulltext finalized on: 8 Nov 2012. This page was last modified: 19 Nov 2012.

© 2012 Mathematical Institute of the Serbian Academy of Science and Arts
© 2012 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition