# Search results for: József Balogh

Journal of Graph Theory > 100 > 3 > 578 - 607

*connected*if all the edges of $M$ are in the same component of $G$. Following Łuczak, there have been many results using the existence of large connected matchings in cluster graphs with respect to regular partitions of large graphs to show the existence of long paths and other structures in these graphs. We prove exact Ramsey‐type bounds on the...

Journal of Graph Theory > 95 > 4 > 655 - 676

*centered*if it is obtained by ‘taking sets as close to the middle layer as possible.’ A poset $P$ is said to have the

*centeredness property*if for any $M$, among all families of size $M$ in $P$, centered families contain the minimum number of comparable pairs. Kleitman showed that the Boolean lattice ${\left\{0,1\right\}}^{n}$ has the centeredness property. It was conjectured...

Journal of Graph Theory > 93 > 1 > 113 - 141

*linear cycle*of length $\ell $, denoted by ${C}_{\ell}^{r}$, is an $r$‐graph with edges ${e}_{1},\text{\u2026},{e}_{\ell}$ such that for every $i\in \left[\ell -1\right],\phantom{\rule{0ex}{0ex}}\mid {e}_{i}\cap {e}_{i+1}\mid =1,\phantom{\rule{0ex}{0ex}}\mid {e}_{\ell}\cap {e}_{1}\mid =1$, and ${e}_{i}\cap {e}_{j}=\varnothing $ for all other pairs $\left\{i,j\right\},\phantom{\rule{0ex}{0ex}}i\ne j$. For every $r\ge 3$ and $\ell \ge 4$, we show that there exists a constant $C$ depending on $r$ and $\ell $ such that the number of linear $r$‐graphs of girth $\ell $ is at most ${2}^{C}$...

Graphs and Combinatorics > 2019 > 35 > 2 > 513-537

*packing*

*k*

*-coloring*of a graph

*G*is a partition of

*V*(

*G*) into sets $$V_1,\ldots ,V_k$$ V 1 , … , V k such that for each $$1\le i\le k$$ 1 ≤ i ≤ k the distance between any two distinct $$x,y\in V_i$$ x , y ∈ V i is at least $$i+1$$ i + 1 . The

*packing chromatic number*, $$\chi _p(G)$$ χ p ( G ) , of a graph

*G*is the minimum

*k*such that

*G*has a packing...

Discrete Applied Mathematics > 2018 > 247 > C > 322-326

Discrete Applied Mathematics > 2018 > 247 > C > 97-101

Chemical Papers > 2019 > 73 > 1 > 165-172

_{3}to F 1:1. The reaction was applied to determine of fluoride. The optimum conditions were achieved at pH...

Journal of Separation Science > 41 > 14 > 2870 - 2877

Discrete Mathematics > 2018 > 341 > 2 > 474-483

Journal of Combinatorial Theory, Series B > 2017 > 126 > C > 83-113

Journal of Combinatorial Theory, Series B > 2017 > 124 > C > 64-87

Israel Journal of Mathematics > 2017 > 219 > 1 > 431-448

*o*(1))(

_{n/2}

^{n}). Later, Burosch–Demetrovics–Katona–Kleitman–Sapozhenko asked for the number

*α*(

*n*) of such families, and they proved that $${2^{\left( {\begin{array}{*{20}{c}} n \\ {n/2} \end{array}}...

Discrete Applied Mathematics > 2016 > 213 > C > 26-33

Random Structures & Algorithms > 49 > 4 > 669 - 693

*n*‐vertex graph

*G*with $\delta \left(G\right)\ge 2n/3$ contains a triangle factor, when $3|n$. In this paper we present two related results that both use the absorbing technique of Rödl, Ruciński and Szemerédi. Our main result determines the minimum degree condition necessary to guarantee a triangle factor in graphs with sublinear independence number. In particular, we...

Random Structures & Algorithms > 49 > 4 > 845 - 872

*t*error correcting codes in $P\left(n\right)$, and we also give an upper bound on the number of transportation codes; Provide an alternative proof of Kleitman's theorem on the number of antichains in $P\left(n\right)$ and give...

Discrete Applied Mathematics > 2016 > 210 > C > 35-37

Random Structures & Algorithms > 48 > 4 > 641 - 654

*K*

_{n}is bipartite. A sparse version of Mantel's Theorem is that, for sufficiently large

*p*, every maximum triangle‐free subgraph of

*G*(

*n, p*) is w.h.p. bipartite. Recently, DeMarco and Kahn proved this for $p>K\sqrt{\mathrm{log}n/n}$ for some constant

*K*, and apart from the value of the constant this...

Combinatorica > 2017 > 37 > 4 > 617-632

*r*∈ℕ, almost every

*n*-vertex

*K*

_{r+1}-free graph is

*r*-partite. In this paper we extend this result to all functions

*r*=

*r*(

*n*) with

*r*⩽ (log

*n*)

^{1/4}. The proof combines a new (close to sharp) supersaturation version of the Erdős-Simonovits stability theorem, the hypergraph container method, and a counting technique developed by Balogh, Bollobás...

Lecture Notes in Computer Science > Graph Drawing > Papers > 25-35

*k*)-sets in a set of points in general position. We then use this to show that if

*S*is a set of

*n*points in general position, then the number □(

*S*) of convex quadrilaterals determined by the points in

*S*is at least $0.37553\binom{n}{4} + O(n^3)$ . This in turn implies that the rectilinear crossing number $\overline{\hbox{\rm...

European Journal of Combinatorics > 2016 > 52 > PA > 47-58