Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 05, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Charlotte Knierim

Resilience of triangle factors in random graphs

In 1963 Corrádi and Hanjal showed that every graph G with minimum degree δ(G)≥ (2/3)n has a triangle factor. Balogh, Lee and Samotij transferred this result to the setting of the random graph G(n,p) and showed that, provided p>> (log n/n)^{1/2}, for a subgraph G ⊆ Γ~ G(n,p) a minimum degree of δ(G)≥(2/3+o(1))np suffices to cover all but O(p^{-2}) vertices in G with disjoint triangles.

We use an idea of Fischer, Škorić, Steger and Trujić and replace the degree condition in the previous result by a lower bound on the number of triangles each vertex is in. We show that in this case for every α > 0 we find a triangle factor provided ((log n)/p)^{1/2} < < p < < n^{-\alpha}.

This masterthesis was supervised by Angelika Steger and Miloš Trujić.

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