This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...
We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...
With the increasing prevalence of massive datasets, it becomes important to design algorithmic techniques for dealing with scenarios where the input to be processed does not fit in the memory of a single machine. Many highly successful approaches have emer ...
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut (MAXCUT) in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communica ...
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 ...
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 ...
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication and ...
Thin-ply composites were shown to exhibit significantly delayed transverse cracking, but the linear onset of damage scaling with ply thickness reported by Amacher et al. (2014) did not correspond to the established LEFM based in situ strength model. This s ...
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 ...
A semi-algebraic graph G = (V, E) is a graph where the vertices are points in R-d, and the edge set E is defined by a semi-algebraic relation of constant complexity on V. In this note, we establish the following Ramsey-Turan theorem: for every integer p >= ...
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 ...
In the 1970s Erdos asked whether the chromatic number of intersection graphs of line segments in the plane is bounded by a function of their clique number. We show the answer is no. Specifically, for each positive integer k we construct a triangle-free fam ...
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 ...
Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...
We consider the complexity of approximation for the INDEPENDENT DOMINATING SET problem in 2P(3)-free graphs, i.e., graphs that do not contain two disjoint copies of the chordless path on three vertices as all induced subgraph. We show that, if P not equal ...
We study complexity and approximation of MIN WEIGHTED NODE COLORING in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove ...
