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- W2892072932 abstract "Given a partition $V_1 sqcup V_2 sqcup dots sqcup V_m$ of the vertex set of a graph, we are interested in finding multiple disjoint independent sets that contain the correct fraction of vertices of each $V_j$. We give conditions for the existence of $q$ such independent sets in terms of the topology of the independence complex. We relate this question to the existence of $q$-fold points of coincidence for any continuous map from the independence complex to Euclidean space of a certain dimension, and to the existence of equivariant maps from the $q$-fold deleted join of the independence complex to a certain representation sphere of the symmetric group. As a corollary we derive the existence of $q$ pairwise disjoint independent sets accurately representing the $V_j$ in certain sparse graphs for $q$ a power of a prime." @default.
- W2892072932 created "2018-09-27" @default.
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- W2892072932 date "2018-09-10" @default.
- W2892072932 modified "2023-09-26" @default.
- W2892072932 title "Fair splittings by independent sets in sparse graphs" @default.
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