6 citations · 9 across the 11 of their papers we have counts for
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Cooperative envy-free division
Duško Jojić, Gaiane Panina, Rade Živaljević
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" and divide…
Envy-free division in the presence of a dragon
Gaiane Panina, Rade Živaljević
We prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive) player, called the "dragon". There are two basic scenarios. 1. Th…
Envy-free division via configuration spaces
Gaiane Panina, Rade Živaljević
The classical approach to envy-free division and equilibrium problems relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree.…
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…
A universality theorem for stressable graphs in the plane
Gaiane Panina
Universality theorems (in the sense of N. Mnëv) claim that the realization space of a combinatorial object (a point configuration, a hyperplane arrangement, a convex polytope, etc.…
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…