In this paper we consider the problem of testing whether a graph is triangle-free, and more generally, whether it is H-free, for a fixed subgraph H. The algorithm should accept gr...
Noga Alon, Tali Kaufman, Michael Krivelevich, Dana...
Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which received recently much attention because of ...
Let X be the random variable that counts the number of triangles in the binomial random graph G(n, p). We show that for some positive constant c, the probability that X deviates f...
We show the first o(n2 ) algorithm for coloring vertices of trianglefree planar graphs using three colors. The time complexity of the algorithm is O(n log n). Our approach can be ...
In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as ...