Almost all k-colorable graphs are easy to color
Journal of Algorithms
The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
The number of graphs without forbidden subgraphs
Journal of Combinatorial Theory Series B
Triple Systems Not Containing a Fano Configuration
Combinatorics, Probability and Computing
The Turán Number Of The Fano Plane
Combinatorica
The typical structure of graphs without given excluded subgraphs
Random Structures & Algorithms
On colourings of hypergraphs without monochromatic fano planes
Combinatorics, Probability and Computing
The structure of almost all graphs in a hereditary property
Journal of Combinatorial Theory Series B
Almost all triple systems with independent neighborhoods are semi-bipartite
Journal of Combinatorial Theory Series A
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The hypergraph of the Fano plane is the unique 3-uniform hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained in a unique triple. This hypergraph is not 2-colorable, but becomes so on deleting any hyperedge from it. We show that taking uniformly at random a labeled 3-uniform hypergraph H on n vertices not containing the hypergraph of the Fano plane, H turns out to be 2-colorable with probability at least 1 -- 2-Ω(n2). For the proof of this result we will study structural properties of Fano-free hypergraphs.