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- Dennis Clemens, Julia Ehrenmüller
- Electr. J. Comb.
- 2016

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)

- Dennis Clemens, Asaf Ferber, Michael Krivelevich, Anita Liebenau
- Combinatorics, Probability & Computing
- 2012

In this paper we analyze classical Maker-Breaker games played on the edge set of a sparse random board G ∼ Gn,p. We consider the Hamiltonicity game, the perfect matching game and the k-connectivity game. We prove that for p(n) ≥ polylog(n)/n, the board G ∼ Gn,p is typically such that Maker can win these games asymptotically as fast as possible, i.e. within… (More)

- Dennis Clemens, Asaf Ferber, Roman Glebov, Dan Hefetz, Anita Liebenau
- SIAM J. Discrete Math.
- 2015

For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T . We prove that if T has bounded maximum degree, then Maker can win this game within n+ 1 moves. Moreover, we prove that Maker can build almost every tree on n vertices… (More)

- Dennis Clemens, Julia Ehrenmüller, Yury Person, Tuan Tran
- Electr. J. Comb.
- 2015

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)

- Dennis Clemens, Yury Person
- Electronic Notes in Discrete Mathematics
- 2015

A uniform hypergraph H is called k-Ramsey for a hypergraph F , if no matter how one colors the edges of H with k colors, there is always a monochromatic copy of F . We say that H is minimal k-Ramsey for F , if H is k-Ramsey for F but every proper subhypergraph of H is not. Burr, Erdős and Lovasz [S. A. Burr, P. Erdős, and L. Lovász, On graphs of Ramsey… (More)

- Dennis Clemens, Mirjana Mikalacki
- Electr. J. Comb.
- 2015

We study the Maker-Breaker tournament game played on the edge set of a given graph G. Two players, Maker and Breaker, claim unclaimed edges of G in turns, while Maker additionally assigns orientations to the edges that she claims. If by the end of the game Maker claims all the edges of a pre-defined goal tournament, she wins the game. Given a tournament Tk… (More)

- Dennis Clemens, Mirjana Mikalacki
- Electronic Notes in Discrete Mathematics
- 2015

We study the (a : a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games – perfect matching game, Hamiltonicity game, star factor game and path factor game, our goal is to determine the least number of moves which Maker needs in order to win these games. Moreover, for all games except for the star… (More)

- Dennis Clemens, Yury Person
- Combinatorics, Probability & Computing
- 2016

- Dennis Clemens, Tuan Tran
- Discrete Mathematics
- 2016

- Dennis Clemens, Julia Ehrenmüller, Yury Person
- Electronic Notes in Discrete Mathematics
- 2016

A Hamilton Berge cycle of a hypergraph on n vertices is an alternating sequence (v1, e1, v2, . . . , vn, en) of distinct vertices v1, . . . , vn and distinct hyperedges e1, . . . , en such that {v1, vn} ⊆ en and {vi, vi+1} ⊆ ei for every i ∈ [n − 1]. We prove a Dirac-type theorem for Hamilton Berge cycles in random r-uniform hypergraphs by showing that for… (More)