Geodesic
Complexes of Directed Trees of Complete Multipartite Graphs
Publications de l'Institut Mathématique, _N_S_92 (2012) no. 106, p. 43 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 $\Delta(\overrightarrow{K}_{n_1,n_2,\ldots,n_k})$.
Classification : 52B22 05C20
Keywords: shellability, directed trees, multipartite graph 
@article{PIM_2012_N_S_92_106_a3,
     author = {Du\v{s}ko Joji\'c},
     title = {Complexes of {Directed} {Trees} of {Complete} {Multipartite} {Graphs}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {43 },
     year = {2012},
     volume = {_N_S_92},
     number = {106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a3/}
}
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Duško Jojić. Complexes of Directed Trees of Complete Multipartite Graphs. Publications de l'Institut Mathématique, _N_S_92 (2012) no. 106, p. 43 . http://geodesic.mathdoc.fr/item/PIM_2012_N_S_92_106_a3/