相关论文: On Upper Bounding Shannon Capacity of Graph Throug…

We prove an upper bound on the Shannon capacity of a graph via a linear programming variation. We show that our bound can outperform both the Lov\'asz theta number and the Haemers minimum rank bound. As a by-product, we also obtain a new…

Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed $\rho$-capacity, that generalizes the Shannon capacity of a graph. We derive upper and lower bounds on the $\rho$-capacity of arbitrary…

For a graph $G$, its $k$-th graph power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$. We consider the problem of deriving upper bounds on the Shannon capacity of graph powers by using spectral…

The Shannon capacity of a graph is a fundamental quantity in zero-error information theory measuring the rate of growth of independent sets in graph powers. Despite being well-studied, this quantity continues to hold several mysteries.…

A vexing open problem in information theory is to find the Shannon capacity of odd cyclic graphs larger than the pentagon and especially for the heptagon. Lower bounds for the capacity are obtained by solving King chess puzzles. Upper…

We investigate the effect of the well-known Mycielski construction on the Shannon capacity of graphs and on one of its most prominent upper bounds, the (complementary) Lov\'asz theta number. We prove that if the Shannon capacity of a graph,…

This paper addresses the behavior of the Lov\'asz number for dense random circulant graphs. The Lov\'asz number is a well-known semidefinite programming upper bound on the independence number. Circulant graphs, an example of a Cayley graph,…

The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product. We show that the series of independence numbers in strong powers of a fixed…

Two classical upper bounds on the Shannon capacity of graphs are the $\vartheta$-function due to Lov\'asz and the minrank parameter due to Haemers. We provide several explicit constructions of $n$-vertex graphs with a constant…

In this note we study Shannon capacity of channels in the context of classical Ramsey numbers. We overview some of the results on capacity of noisy channels modelled by graphs, and how some constructions may contribute to our knowledge of…

In this paper, we give spectral upper bounds for the independence number of even uniform hypergraphs and graphs, extend the Hoffman bound to even uniform hypergraphs, and give a simple spectral condition for determining the independence…

In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…

The capacity of a graph is defined as the rate of exponential grow of independent sets in the strong powers of the graph. In strong power, an edge connects two sequences if at each position letters are equal or adjacent. We consider a…

The Lov\'{a}sz theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a maximal clique, and so one can instead apply this…

We introduce a generalization of the celebrated Lov\'asz theta number of a graph to simplicial complexes of arbitrary dimension. Our generalization takes advantage of real simplicial cohomology theory, in particular combinatorial…

This paper provides new observations on the Lov\'{a}sz $\theta$-function of graphs. These include a simple closed-form expression of that function for all strongly regular graphs, together with upper and lower bounds on that function for…

The theta function of Lovasz is a graph parameter that can be computed up to arbitrary precision in polynomial time. It plays a key role in algorithms that approximate graph parameters such as maximum independent set, maximum clique and…

In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…

This paper delves into three research directions, leveraging the Lov\'{a}sz $\vartheta$-function of a graph. First, it focuses on the Shannon capacity of graphs, providing new results that determine the capacity for two infinite subclasses…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…