Results 61 to 70 of about 13,803 (191)

Combinatorial theorems relative to a random set [PDF]

, 2014
We describe recent advances in the study of random analogues of combinatorial theorems.Comment: 26 pages.
Conlon, David
core   +2 more sources

Undecidability of polynomial inequalities in weighted graph homomorphism densities

Forum of Mathematics, Sigma
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights.
Grigoriy Blekherman, Annie Raymond, Fan Wei   +2 more
doaj   +1 more source

Hamilton cycles in graphs and hypergraphs: an extremal perspective [PDF]

, 2014
As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi ...
Kühn, Daniela, Osthus, Deryk
core   +1 more source

The Turán problem for hypergraphs of fixed size [PDF]

, 2005
We obtain a general bound on the Turán density of a hypergraph in terms of the number of edges that it contains. If F is an r-uniform hypergraph with f edges we show that [pi](F) =3 and f->[infinity]
Keevash, Peter
core  

SPERNER THEOREMS FOR UNRELATED COPIES OF POSETS AND GENERATING DISTRIBUTIVE LATTICES

Ural Mathematical Journal
For a finite poset (partially ordered set) \(U\) and a natural number \(n\), let \(S(U,n)\) denote the largest number of pairwise unrelated copies of  \(U\) in the powerset lattice (AKA subset lattice) of an \(n\)-element set.
Gábor Czédli
doaj   +1 more source

Discrete Extremal Length and Cube Tilings in Finite Dimensions

, 2014
Extremal length is a conformal invariant that transfers naturally to the discrete setting, giving square tilings as a natural combinatorial analog of conformal mappings. Recent work by S.
Wood, William E.
core   +1 more source

Linear trees in uniform hypergraphs [PDF]

, 2013
Given a tree T on v vertices and an integer k exceeding one. One can define the k-expansion T^k as a k-uniform linear hypergraph by enlarging each edge with a new, distinct set of (k-2) vertices. Then T^k has v+ (v-1)(k-2) vertices. The aim of this paper
Furedi, Zoltan
core  

Geometric variational problems of statistical mechanics and of combinatorics

, 2000
We present the geometric solutions of the various extremal problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape of a ...
Alexander K., Ioffe D., Ioffe D., Ioffe D., Senya Shlosman, Taylor J. E., Vershik A., Vershik A., Vershik A., Wulff G.   +9 more
core   +2 more sources

Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Discrete Analysis, 2017
Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case, Discrete Analysis 2017:5, 34 pp. Szemerédi's theorem, proved in 1975, asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every subset
Sean Prendiville
doaj   +1 more source

Quasirandom Cayley graphs

Discrete Analysis, 2017
Quasirandom Cayley graphs, Discrete Analysis 2017:6, 14 pp. An extremely important phenomenon in extremal combinatorics is that of _quasirandomness_: for many combinatorial structures, it is possible to identify a list of deterministic properties, each ...
David Conlon, Yufei Zhao
doaj   +1 more source