Results for "Balázs Patkós"
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Finding non-minority balls with majority and plurality queriesDec 20 2018Given a set of $n$ colored balls, a \textit{majority, non-minority or plurality ball} is one whose color class has size more than $n/2$, at least $n/2$ or larger than any other color class, respectively. We describe linear time algorithms for finding ... More t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More Large B_d-free and union-free subfamiliesDec 17 2010For a property $\Gamma$ and a family of sets $\cF$, let $f(\cF,\Gamma)$ be the size of the largest subfamily of $\cF$ having property $\Gamma$. For a positive integer $m$, let $f(m,\Gamma)$ be the minimum of $f(\cF,\Gamma)$ over all families of size $m$. ... More Avoider-Enforcer star gamesFeb 11 2013Jan 30 2015In this paper, we study $(1 : b)$ Avoider-Enforcer games played on the edge set of the complete graph on $n$ vertices. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. ... More Two-part set systemsOct 01 2011The two part Sperner theorem of Katona and Kleitman states that if $X$ is an $n$-element set with partition $X_1 \cup X_2$, and $\cF$ is a family of subsets of $X$ such that no two sets $A, B \in \cF$ satisfy $A \subset B$ (or $B \subset A$) and $A \cap ... More Nonrepetitive colorings of lexicographic product of graphsOct 20 2012Sep 16 2013A coloring $c$ of the vertices of a graph $G$ is nonrepetitive if there exists no path $v_1v_2\ldots v_{2l}$ for which $c(v_i)=c(v_{l+i})$ for all $1\le i\le l$. Given graphs $G$ and $H$ with $|V(H)|=k$, the lexicographic product $G[H]$ is the graph obtained ... More Search Problems in Vector SpacesSep 26 2013Jan 30 2014We consider the following $q$-analog of the basic combinatorial search problem: let $q$ be a prime power and $\GF(q)$ the finite field of $q$ elements. Let $V$ denote an $n$-dimensional vector space over $\GF(q)$ and let $\mathbf{v}$ be an unknown 1-dimensional ... More Line Percolation in Finite Projective PlanesAug 01 2016We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the ... More Majority and Plurality ProblemsMar 07 2012Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. ... More Cross-Sperner familiesApr 20 2011A pair of families $(\cF,\cG)$ is said to be \emph{cross-Sperner} if there exists no pair of sets $F \in \cF, G \in \cG$ with $F \subseteq G$ or $G \subseteq F$. There are two ways to measure the size of the pair $(\cF,\cG)$: with the sum $|\cF|+|\cG|$ ... More Domination game on uniform hypergraphsOct 01 2017In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the set of vertices ... More Finding a non-minority ball with majority answersSep 28 2015Sep 28 2016Suppose we are given a set of $n$ balls $\{b_1,\ldots,b_n\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\{b_{i_1},b_{i_2},b_{i_3}\}$. As an answer to such ... More Saturating Sperner familiesMay 23 2011A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still satisfied by the resulting family. We address the problem of finding the minimum ... More Grundy dominating sequences and zero forcing setsFeb 02 2017In a graph $G$ a sequence $v_1,v_2,\dots,v_m$ of vertices is Grundy dominating if for all $2\le i \le m$ we have $N[v_i]\not\subseteq \cup_{j=1}^{i-1}N[v_j]$ and is Grundy total dominating if for all $2\le i \le m$ we have $N(v_i)\not\subseteq \cup_{j=1}^{i-1}N(v_j)$. ... More Dominating sequences in grid-like and toroidal graphsJul 01 2016A longest sequence $S$ of distinct vertices of a graph $G$ such that each vertex of $S$ dominates some vertex that is not dominated by its preceding vertices, is called a Grundy dominating sequence; the length of $S$ is the Grundy domination number of ... More Forbidding rank-preserving copies of a posetOct 25 2017The maximum size, $La(n,P)$, of a family of subsets of $[n]=\{1,2,...,n\}$ without containing a copy of $P$ as a subposet, has been intensively studied. Let $P$ be a graded poset. We say that a family $\mathcal{F}$ of subsets of $[n]=\{1,2,...,n\}$ contains ... More The Wiedemann-Franz law in the SU(N) Wolff modelFeb 16 2006We study the electrical and thermal transport through the SU(N) Wolff model with the use of bosonization. The Wilson ratio reaches unity as N grows to infinity. The electric conductance is dominated by the charge channel, and decreases monotonically with ... More Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Oct 26 2016The main result is that the possible algebraic degrees of pseudo-Anosov stretch factors on the closed orientable surface of genus $g$ are the even integers between 2 and $6g-6$ and the odd integers between 3 and $3g-3$. There is an analogous result for ... More Covering Paths and Trees for Planar GridsNov 03 2013Given a set of points in the plane, a covering path is a polygonal path that visits all the points. In this paper we consider covering paths of the vertices of an n x m grid. We show that the minimal number of segments of such a path is $2\min(n,m)-1$ ... More Spin supplementary conditions for spinning compact binariesSep 06 2016We consider the different spin supplementary conditions (SSC) for a spinning compact binary with the leading-order spin-orbit (SO) interaction. The Lagrangian of the binary system can be constructed but it is acceleration-dependent in two cases of SSC. ... More On the Ledrappier-Young formula for self-affine measuresMar 03 2015Jun 02 2015Ledrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier-Young ... More Characterizations and Properties of Graphs of Baire FunctionsNov 02 2016Let $X$ be a paracompact topological space and $Y$ be a Banach space. In this paper, we will characterize the Baire-1 functions $f:X\rightarrow{Y}$ by their graph: namely, we will show that $f$ is a Baire-1 function if and only if its graph $gr(f)$ is ... More Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Nov 19 2016The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface $S$ can be as high as the dimension of the Teichm\"uller space of $S$. In addition to proving this, we completely ... More Mixing time of an unaligned Gibbs sampler on the squareJun 27 2017Oct 06 2018The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square $[0,1]^2$ to approach a stationary distribution with density proportional to $\exp(-A^2(u-v)^2)$ for $(u,v)\in ... More Baire categorical aspects of first passage percolationNov 21 2017In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability measure defined ... More An implementation of the relational k-means algorithmApr 25 2013A C# implementation of a generalized k-means variant called relational k-means is described here. Relational k-means is a generalization of the well-known k-means clustering method which works for non-Euclidean scenarios as well. The input is an arbitrary ... More The Fermi edge singularity in the SU(N) Wolff modelSep 15 2005The low temperature properties of the SU(N) Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low temperature properties of the model. The single particle Green's function ... More Algebraic degrees of pseudo-Anosov stretch factorsJun 21 2015Oct 16 2018The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface $S$ can be as high as the dimension of the Teichm\"uller space of $S$. In addition to proving this, we completely ... More Baire categorical aspects of first passage percolation IINov 11 2018In this paper we continue our earlier work about topological first passage percolation and answer certain questions asked in our previous paper. Notably, we prove that apart from trivialities, in the generic configuration there exists exactly one geodesic ... More Boundary effect on CDW: Friedel oscillations, STM imageMar 17 2005We study the effect of open boundary condition on charge density waves (CDW). The electron density oscillates rapidly close to the boundary, and additional non-oscillating terms (~ln(r)) appear. The Friedel oscillations survive beyond the CDW coherence ... More Coloring half-planes and bottomless rectanglesMay 01 2011We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this problem is that ... More The variety of domination gamesJul 07 2018Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by two players, named Dominator and Staller. In this paper, Z-domination ... More On Grundy total domination number in product graphsDec 23 2017A longest sequence $(v_1,\ldots,v_k)$ of vertices of a graph $G$ is a Grundy total dominating sequence of $G$ if for all $i$, $N(v_i) \setminus \bigcup_{j=1}^{i-1}N(v_j)\not=\emptyset$. The length $k$ of the sequence is called the Grundy total domination ... More Effective Models of the Electroweak Phase TransitionJun 06 1995The consecutive integration over the distinct mass scales ${\cal O}(T),{\cal O}(gT)$ leads to a hierarchy of effective models for the electroweak phase transition. Different techniques for the realisation of such strategy are reviewed. Advantages and ... More Magnetotransport and thermoelectricity in disordered grapheneJan 29 2007We have studied the electric and thermal response of two-dimensional Dirac-fermions in a quantizing magnetic field in the presence of localized disorder. The electric and heat current operators in the presence of magnetic field are derived. The self-energy ... More NMR relaxation rate and static spin susceptibility in grapheneFeb 17 2008The NMR relaxation rate and the static spin susceptibility in graphene are studied within a tight-binding description. At half filling, the NMR relaxation rate follows a power law as $T^2$ on the particle-hole symmetric side, while with a finite chemical ... More Improved mixing rates of directed cycles by added connectionSep 04 2015Sep 16 2015We provide bounds on the mixing rate of a Markov chain whose mixing properties are improved by a combination of adding long distance edges and introducing non-reversibility. Our model is built on a cycle graph and involves selecting a sublinear number ... More Harmonic Manifolds and the Volume of Tubes about CurvesJun 08 2015Oct 03 2016H. Hotelling proved that in the n-dimensional Euclidean or spherical space, the volume of a tube of small radius about a curve depends only on the length of the curve and the radius. A. Gray and L. Vanhecke extended Hotelling's theorem to rank one symmetric ... More Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs ModelMar 05 1996We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading ... More Reentrant Kondo effect in Landau quantized grapheneMay 14 2007We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical ... More AMS-02 fits Dark MatterSep 07 2015May 10 2016In this work we perform a comprehensive statistical analysis of the AMS-02 electron, positron fluxes and the antiproton-to-proton ratio in the context of a simplified dark matter model. We include known, standard astrophysical sources and a dark matter ... More More on Decomposing Coverings by OctantsMar 05 2015Nov 17 2015In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering ... More Convex Polygons are Self-CoverableJul 09 2013Mar 14 2014We introduce a new notion for geometric families called self-coverability and show that homothets of convex polygons are self-coverable. As a corollary, we obtain several results about coloring point sets such that any member of the family with many points ... More Path-search in the pyramid and in other graphsApr 27 2011We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every ... More Octants are Cover DecomposableJan 19 2011Jan 20 2011We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold covering of any subset ... More Limits of compact decorated graphsOct 25 2010Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an element of a ... More Regularity partitions and the topology of graphonsFeb 23 2010We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this metric space to ... More On the Question of Validity of the Anthropic PrinciplesSep 18 2006During the last centuries of human history, many questions was repeated in connection with the great problems of the existence and origin of human beings, and also of the Universe. The old questions of common sense and philosophy have not been solved ... More Stochastic integration based on simple, symmetric random walksDec 23 2007Jul 06 2009A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less ... More The graph theoretic moment problemOct 25 2010We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space. Among other things ... More Random Graphons and a Weak Positivstellensatz for GraphsFeb 08 2009In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency conditions, and normalized, ... More Improved mixing rates of directed cycles by added connectionSep 04 2015Feb 10 2018We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced: as a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all ... More Electron spin dynamics in strongly correlated metalsJan 28 2009The temperature dependence of the electron spin life-time, T_1 and the g-factor are anomalous in alkali fullerides (K,Rb)_3C_60, which cannot be explained by the canonical Elliott-Yafet theory. These materials are archetypes of strongly correlated and ... More Dimension maximizing measures for self-affine systemsJul 10 2015Apr 26 2016In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (K\"aenm\"aki ... More On the transience of random interlacementsFeb 23 2011Jul 17 2011We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these ... More Proper Coloring of Geometric HypergraphsDec 07 2016We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of ... More Minimal Penner dilatations on nonorientable surfacesJul 24 2018For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast ... More Harmonic Manifolds and TubesApr 30 2017Jul 23 2017The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius. In this paper, we show that this ... More Inelastic Scattering from Local Vibrational ModesJun 10 2008We study a nonuniversal contribution to the dephasing rate of conduction electrons due to local vibrational modes. The inelastic scattering rate is strongly influenced by multiphonon excitations, exhibiting oscillatory behaviour. For higher frequencies, ... More