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We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…
We analyse uniformly random proper $k$-colourings of sparse graphs with maximum degree $\Delta$ in the regime $\Delta < k\ln k $. This regime corresponds to the lower side of the shattering threshold for random graph colouring, a…
Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…
To compute the hyperbolicity constant is an almost intractable problem, thus it is natural to try to bound it in terms of some parameters of the graph. Let $\mathcal{G}(g,c,n)$ be the set of graphs $G$ with girth $g(G)=g$, circumference…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
Many networked systems involve multiple modes of transport. Such systems are called multimodal, and examples include logistic networks, biomedical phenomena, manufacturing process and telecommunication networks. Existing techniques for…
We propose a new proof technique that aims to be applied to the same problems as the Lov\'asz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve…
We reprove the results on the hardness of approximating hypergraph coloring using a different technique based on bounds on the size of extremal $t$-agreeing families of $[q]^n$. Specifically, using theorems of Frankl-Tokushige [FT99],…
We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
A $b$-coloring of a graph $G$ is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The b-Coloring problem asks whether a graph $G$ has a…
Recent improvements on the deterministic complexities of fundamental graph problems in the LOCAL model of distributed computing have yielded state-of-the-art upper bounds of $\tilde{O}(\log^{5/3} n)$ rounds for maximal independent set (MIS)…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in…
We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all $q \ge 2$. This immediately…
Recent breakthroughs in graph streaming have led to the design of single-pass semi-streaming algorithms for various graph coloring problems such as $(\Delta+1)$-coloring, degeneracy-coloring, coloring triangle-free graphs, and others. These…
The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the…
Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…