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Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on ...
We answer some questions raised by Gantert, Lowe and Steif (Ann. Inst. Henri Poincare Probab. Stat. 41 (2005) 767 780) concerning "signed" voter models on locally finite graphs. These are voter model like processes with the difference that the edges are co ...
We prove that every 3-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a set of order ohm(n(1/3) log(2) n) which uses at most two colors, and this bound is tight up to a constant factor. This verifies a conjectu ...
Approximate graph matching (AGM) refers to the problem of mapping the vertices of two structurally similar graphs, which has applications in social networks, computer vision, chemistry, and biology. Given its computational cost, AGM has mostly been limited ...
Let F be a graph. A hypergraph is called Berge-F if it can be obtained by replacing each edge in F by a hyperedge containing it. Let F be a family of graphs. The Turan number of the family Berge-F is the maximum possible number of edges in an r-uniform hyp ...
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs defined by geometric representations and competitivity analysis of on-line algorithms. This connection became apparent after the recent construction ...
We study complexity issues related to some coloring problems in grids: we examine in particular the case of List coloring, of Precoloring extension and of (p, q)-List coloring, the case of List coloring in bipartite graphs where lists in the first part of ...
We consider the problem of inferring the hidden structure of high-dimensional dynamic systems from the perspective of graph learning. In particular, we aim at capturing the dynamic relationships between nodes by a sequence of graphs. Our approach is motiva ...
