polytope theory, Kalai's 3d conjecture is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989. It states...

Commons has media related to Gil Kalai (mathematician). Kalai's home page at Hebrew University Combinatorics and more, Kalai's blog "Noise stability, noise...

mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered monetary rewards for solving them. The Erdős–Gyárfás conjecture on cycles...

Sumner Byron Myers Prize for his PhD thesis. In 2009, during his PhD studies, Huh proved the Read–Hoggar conjecture, about the unimodality of coefficients...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

Unsolved problem in mathematics Conjecture: If k complete graphs, each having exactly k vertices, have the property that every pair of complete graphs...

Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph...

A counterexample to the conjecture was discovered by Yaroslav Shitov (2019) (see Kalai 2019), thus disproving the conjecture in general. Any graph with...

Improving lower and upper bounds for the Heilbronn triangle problem. Kalai's 3d conjecture on the least possible number of faces of centrally symmetric polytopes...

Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d. That...

/ d ) {\displaystyle g_{d}(n)=O(n^{2/d})} and conjectured that the upper bound is in fact sharp, i.e., g d ( n ) = Θ ( n 2 / d ) {\displaystyle g_{d}(n)=\Theta...

triangulations of space. Gil Kalai for making progress on the Hirsch conjecture by proving subexponential bounds on the diameter of d-dimensional polytopes with...

the proofs of Kneser's conjecture and the Lovász local lemma, as well as the formulation of the Erdős–Faber–Lovász conjecture. He is also one of the eponymous...

structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ-boundedness, and the Erdős–Hajnal conjecture. Many of his recent papers...

Hirsch conjecture, now disproved, suggested a strong (linear) bound on how large the diameter of a polytope with fixed dimension d {\displaystyle d} and...

33. The Hanner polytopes form an important class of examples for Kalai's 3d conjecture that all centrally symmetric polytopes have at least 3d nonempty...

not on level d {\displaystyle d} . We similarly define f > d , f < d , f ≥ d , f ≤ d {\displaystyle f^{>d},f^{<d},f^{\geq d},f^{\leq d}} . The i {\displaystyle...

positivity". arXiv:1812.10454 [math.CO]. Kalai, Gil (2018-12-25). "Amazing: Karim Adiprasito proved the g-conjecture for spheres!". Combinatorics and more...

Interdependent networks – Subfield of network science Invasion percolation Kahn–Kalai conjecture – Mathematical proposition Network theory – Study of graphs as a representation...

edges, where c(k) is a constant depending only on k. This conjecture is known to be true for k = 3 and k = 4. It is also known to be true for convex geometric...

m e ( m o d n ) {\displaystyle c:=m^{e}(\mathrm {mod} \;n)} , the RSA problem is to find m {\displaystyle m} . The problem is conjectured to be hard...

for ovoidal Möbius planes. In 1993, together with Gil Kalai, he disproved Borsuk's conjecture. In 1996 he was awarded the Pólya Prize (SIAM). He was...

Hadwiger's conjecture", Journal of Combinatorial Theory, Series B, 99 (1): 20–29, doi:10.1016/j.jctb.2008.03.006, MR 2467815. Chudnovsky, Maria; Kalai, Gil;...

Mathematics, 35 (3): 236–238, doi:10.1016/0001-8708(80)90050-X, MR 0563925. Kalai, Gil (2018-12-25). "Amazing: Karim Adiprasito proved the g-conjecture for spheres...

determined by its 1-skeleton; his conjecture was proven in 1987 by Roswitha Blind and Peter Mani-Levitska. Gil Kalai shortly after provided a simpler proof...

problem can be shown equivalent to Connes embedding problem, a famous conjecture in the theory of operator algebras. Since the dimensions of H A {\displaystyle...

Blotto game). Borel conjectured the non-existence of mixed-strategy equilibria in finite two-person zero-sum games, a conjecture that was proved false...

polytopes formed a class of important examples for the Mahler conjecture and for Kalai's 3d conjecture. In another paper from the same year, Hanner proved a set...

overhead present in classical simulations, validating Feynman's 1982 conjecture. Over the years, experimentalists have constructed small-scale quantum...

162, Issue 3, pp 431–461 doi:10.1007/s00440-014-0576-6 A proof of the block model threshold conjecture, Combinatorica, 2018, Volume 38, Issue 3, pp 665-708...