7 papers
Splitting necklaces, with constraints
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove several versions of N. Alon's "necklace-splitting theorem", subject to additional constraints, as illustrated by the following results. (1) The "almost equicardinal neckla…
The cubical matching complex revisited
Duško Jojić
Ehrenborg noted that all tilings of a bipartite planar graph are encoded by its cubical matching complex and claimed that this complex is collapsible. We point out to an oversight…
A Tverberg type theorem for collectively unavoidable complexes
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove (Theorem 2.4) that the symmetrized deleted join of a "balanced family" of collectively -unavoidabl…
Symmetric multiple chessboard complexes and a new theorem of Tverberg type
Duško Jojić, Siniša Vrećica, Rade Živaljević
We prove a new theorem of Tverberg type which confirms the conjecture of Blagojevic, Frick, and Ziegler about the existence of "balanced Tverberg partitions" (Conjecture 6.6 in, Tv…
Multiple chessboard complexes and the colored Tverberg problem
Duško Jojić, Siniša T. Vrećica, Rade T. Živaljević
Following D.B. Karaguezian, V. Reiner, and M.L. Wachs (Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of -Complexes, Journal of Algebra 2001) we study th…
Generalized Dehn-Sommerville relations for hypergraphs
Vladimir Grujic, Tanja Stojadinovic, Dusko Jojic
The generalized Dehn-Sommerville relations determine the odd subalgebra of the combinatorial Hopf algebra. We introduce a class of eulerian hypergraphs that satisfy the generalized…
Shellability of complexes of directed trees
Duško Jojić
The question of shellability of complexes of directed trees was asked by R. Stanley. D. Kozlov showed that the existence of a complete source in a directed graph provides a shellin…