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A slight modification of the proof of Szemerédi’s cube lemma gives that if a set $S \subset [1, n]$ satisfies $| S | \geq \frac{n}{2}$ , then $S$ must contain a non-degenerate Hilbert cube of dimension $⌊ {log}_{2} {log}_{2} n - 3 ⌋$ . In this paper we prove that in a random set $S$ determined by $\Pr {s \in S} = \frac{1}{2}$ for $1 \leq s \leq n$ , the maximal dimension of non-degenerate Hilbert cubes is a.e. nearly ${log}_{2} {log}_{2} n + {log}_{2} {log}_{2} {log}_{2} n$ and determine the threshold function for a non-degenerate $k$ -cube.

Nonderogatory directed windmills.

Rada, Juán (2008)

Revista Colombiana de Matemáticas

Nonderogatory unicyclic digraphs.

Bravo, Diego, Rada, Juan (2007)

International Journal of Mathematics and Mathematical Sciences

Nonempty intersection of longest paths in a graph with a small matching number

Fuyuan Chen (2015)

Czechoslovak Mathematical Journal

A maximum matching of a graph $G$ is a matching of $G$ with the largest number of edges. The matching number of a graph $G$ , denoted by $α^{'} (G)$ , is the number of edges in a maximum matching of $G$ . In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Although this conjecture has been disproved, finding some nice classes of graphs that support this conjecture is still very meaningful and interesting. In this short note, we prove that Gallai’s conjecture is true for...

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Non-canonical extensions of Erdős-Ginzburg-Ziv theorem.

Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I: Generalizations of the Capelli and Turnbull identities.

Noncommutative Sylvester's determinantal identity.

Noncommutative symmetric functions. III: Deformations of Cauchy and convolution algebras.

Non-complete extended $P$ -sum of graphs, graph angles and star partitions.

Non-constant continuous mappings of metric or compact Hausdorff spaces

Noncovering of multiples.

Noncrossing partitions, clusters and the Coxeter plane.

Noncrossing trees and noncrossing graphs.

Non-degenerate Hilbert cubes in random sets

Nonderogatory directed windmills.

Nonderogatory unicyclic digraphs.

Nonempty intersection of longest paths in a graph with a small matching number

Nonexistence of almost Moore digraphs of diameter three.

Nonexistence of graphs with cyclic defect.

Non-Existence of Steiner Systems of Type S (d - 1, d, 2d).

Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected $P_{3}$ -graphs.

Nonexistence of twentieth power residue difference sets

Nonexistence results for Hadamard-like matrices.

Non-Hamiltonian Square-minus-two.

Currently displaying 101 – 120 of 227