相关论文: Quantum Complexity Bounds for Independent Set Prob…

We derive algebraic bounds on achievable rates for quantum state transfer and entanglement generation in general quantum systems. We apply these bounds to graph-based models of local quantum spin systems to obtain speed limits on these…

We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given…

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…

We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.

Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…

Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…

The inertia bound, introduced by Cvetkovi\'c in 1971, is a fundamental result in spectral graph theory that provides an upper bound for the independence number of a graph in terms of spectral information about a weighted adjacency matrix of…

We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…

We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…

We determine the maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers and we completely characterize the extremal graphs. As an application, we give a similar result for K\"onig-Egerv\'ary graphs…

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…

Let G be a graph. The independence-domination number is the maximum over all independent sets I in G of the minimal number of vertices needed to dominate I. In this paper we investigate the computational complexity of independence…

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…

Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos…

Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…

We study the problem of maximizing the number of independent sets in $n$-vertex $k$-chromatic $\ell$-connected graphs. First we consider maximizing the total number of independent sets in such graphs with $n$ sufficiently large, and for…

In [1] the problem of finding a sharp lower bound on lower against number of a general graph is mentioned as an open question. We solve the problem by establishing a tight lower bound on lower against number of a general graph in terms of…

The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…

We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…

Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…