相关论文: Applications of graph containers in the Boolean la…
In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem). We have developed an efficient algorithm for light spanners in bounded pathwidth graphs, based…
We investigate the maximum size of graph families on a common vertex set of cardinality $n$ such that the symmetric difference of the edge sets of any two members of the family satisfies some prescribed condition. We solve the problem…
Recently, Letzter proved that any graph of order $n$ contains a collection $\mathcal{P}$ of $O(n\log^\star n)$ paths with the following property: for all distinct edges $e$ and $f$ there exists a path in $\mathcal{P}$ which contains $e$ but…
In this paper, we examine roots of graph polynomials where those roots can be considered as structural graph measures. More precisely, we prove analytical results for the roots of certain modified graph polynomials and also discuss…
In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily…
We calculate the conductivity of arbitrarily stacked multilayer graphene sheets within a relaxation time approximation, considering both short-range and long-range impurities. We theoretically investigate the feasibility of identifying the…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a…
In recent breakthrough results, Saxton--Thomason and Balogh--Morris--Samotij have developed powerful theories of hypergraph containers. These theories have led to a large number of new results on transference, and on counting and…
In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated…
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the code, the number of reads used in the reconstruction…
We probe the accuracy limit of {\it ab initio} calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
Let $P$ be a poset of size $2^k$ that has a greatest and a least element. We prove that, for sufficiently large $n$, the Boolean lattice $2^{[n]}$ can be partitioned into copies of $P$. This resolves a conjecture of Lonc.
There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…
Gottesman-Kitaev-Preskill (GKP) codes are a promising candidate for implementing fault tolerant quantum computation in quantum harmonic oscillator systems such as superconducting resonators, optical photons and trapped ions, and in recent…
We provide a short proof of a conic version of the colorful Carath\'eodory theorem for oriented matroids. Holmsen's extension of the colorful Carath\'eodory theorem to oriented matroids (Advances in Mathematics, 2016) already encompasses…
In this paper we show that for any poset $P$ that is not an antichain, the number of induced $P$-free families in the Boolean lattice $2^{[n]}$ is at most $ 2^{O(\mathrm{La}^*(n,P))}$, where $\mathrm{La}^*(n,P)$ denotes the the largest size…
A layered graph $G^\times$ is the Cartesian product of a graph $G = (V,E)$ with the linear graph $Z$, e.g. $Z^\times$ is the 2D square lattice $Z^2$. For Bernoulli percolation with parameter $p \in [0,1]$ on $G^\times$ one intuitively would…
We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…