The vertex set of the Kneser graph K(n, k) is V = (([n])(k)) and two vertices are adjacent if the corresponding sets are disjoint. For any graph F, the largest size of a vertex set U subset of V such that K(n, k)[U] is F-free, was recently determined by Al ...
A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...
Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...
Many modern services need to routinely perform tasks on a large scale. This prompts us to consider the following question:How can we design efficient algorithms for large-scale computation?In this thesis, we focus on devising a general strategy to addr ...
In this paper, we address the resource allocation problem of device-to-device (D2D) communications underlaying orthogonal frequency division multiple access (OFDMA) based cellular systems by exploiting the efficiency that comes from an ensemble of graph th ...
We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with a(n) memory per machine, that compute a maximal independent set, a 1 + epsilon approximation of maximum matching, and a 2 + epsilon approximation of minimum ve ...
A classic result of Erdos, Gyarfas and Pyber states that for every coloring of the edges of K-n with r colors, there is a cover of its vertex set by at most f(r)=O(r2logr) vertex-disjoint monochromatic cycles. In particular, the minimum number of such cove ...
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph counting has been ...
In this paper we propose a novel vertex based sampling method for k-bandlimited signals lying on arbitrary graphs, that has a reasonable computational complexity and results in low reconstruction error. Our goal is to find the smallest set of vertices that ...
