Julia Ehrenmüller

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A conjecture by Aharoni and Berger states that every family of n matchings of size n + 1 in a bipartite multigraph contains a rainbow matching of size n. In this paper we prove that matching sizes of ( 3 2 + o(1) ) n suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best-known one in the case where we only aim to(More)
We consider biased (1 : b) Avoider-Enforcer games in the monotone and strict versions. In particular, we show that Avoider can keep his graph being a forest for every but maybe the last round of the game if b > 200n lnn. By this we obtain essentially optimal upper bounds on the threshold biases for the non-planarity game, the non-k-colorability game, and(More)
In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersection. This is not true in general and various counterexamples have been found. However, the answer to Gallai’s question is positive for several well-known classes of graphs, as for instance connected outerplanar graphs, connected split graphs, and 2-trees. A graph is(More)
For each real γ > 0 and integers ∆ ≥ 2 and k ≥ 1, we prove that there exist constants β > 0 and C > 0 such that for all p ≥ C(log n/n)1/∆ the random graph G(n, p) asymptotically almost surely contains even after an adversary deletes an arbitrary (1/k − γ)-fraction of the edges at every vertex a copy of every nvertex graph with maximum degree at most ∆,(More)
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