Geodesic
Complexes of Directed Trees of Complete Multipartite Graphs
Publications de l'Institut Mathématique, _N_S_92 (2012) no. 106, p. 43

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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/
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     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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