PreprintCC BY 4.0HAL
A HELLY-TYPE THEOREM FOR TWO-COMPONENT CONVEX SETS
Abstract
In any fixed dimension, consider a finite collection of sets, each consisting of exactly two disjoint, closed, convex pieces. We show that to guarantee the intersection of the whole collection also consists of exactly two such convex pieces, it suffices to verify the same two-piece structure for all intersections of some subfamilies of intermediate size, thus answering a question of Gil Kalai.
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BibTeX
@misc{menara2026hellytype,
title = {{A HELLY-TYPE THEOREM FOR TWO-COMPONENT CONVEX SETS}},
author = {Giuliamaria Menara},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05737724v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A HELLY-TYPE THEOREM FOR TWO-COMPONENT CONVEX SETS
AU - Giuliamaria Menara
PY - 2026
DA - 2026/09/03
PB - HAL
UR - https://hal.science/hal-05737724v1
AB - In any fixed dimension, consider a finite collection of sets, each consisting of exactly two disjoint, closed, convex pieces. We show that to guarantee the intersection of the whole collection also consists of exactly two such convex pieces, it suffices to verify the same two-piece structure for all intersections of some subfamilies of intermediate size, thus answering a question of Gil Kalai.
ER -