Christian Reiher

activity

20162026

most citedHypergraphs with many extremal configurations

7 citations · 13 across the 23 of their papers we have counts for

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Showing 2020Show all

7 papers · 1 filter

math.CO2020

On quantitative aspects of a canonisation theorem for edge-orderings

Christian Reiher, Vojtěch Rödl, Marcelo Sales +2

For integers $k \geq 2$ and $N \geq 2 k + 1$ there are $k! 2^{k}$ canonical orderings of the edges of the complete $k$ -uniform hypergraph with vertex set $[N] = {1, 2, \dots, N}$ . These are…

math.CO2020

Sandwiching biregular random graphs

Tereza Klimošová, Christian Reiher, Andrzej Ruciński +1

Let $G (n, n, m)$ be a uniformly random $m$ -edge subgraph of the complete bipartite graph $K_{n, n}$ with bipartition $(V_{1}, V_{2})$ , where $n_{i} = ∣ V_{i} ∣$ . Given a real number $p \in [0,1…

math.CO2020

On Hamiltonian cycles in hypergraphs with dense link graphs

Joanna Polcyn, Christian Reiher, Vojtěch Rödl +1

We show that every $k$ -uniform hypergraph on $n$ vertices whose minimum $(k - 2)$ -degree is at least $(5/9 + o (1)) n^{2} /2$ contains a Hamiltonian cycle. A construction due to Han and Zha…

math.CO2020

Minimum pair degree condition for tight Hamiltonian cycles in $4$ -uniform hypergraphs

Joanna Polcyn, Christian Reiher, Vojtěch Rödl +3

We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9 + o (1)) n^{2} /2$ contains a tight Hamiltonian cycle. This degree condition is asymptotic…

math.CO2020

High powers of Hamiltonian cycles in randomly augmented graphs

Sylwia Antoniuk, Andrzej Dudek, Christian Reiher +2

We investigate the existence of powers of Hamiltonian cycles in graphs with large minimum degree to which some additional edges have been added in a random manner. For all integers…

math.CO2020

Andrásfai and Vega graphs in Ramsey-Turán theory

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

Given positive integers $n \geq s$ , we let $ex (n, s)$ denote the maximum number of edges in a triangle-free graph $G$ on $n$ vertices with $α (G) \leq s$ . In the early sixties…

On quantitative aspects of a canonisation theorem for edge-orderings

Sandwiching biregular random graphs

On Hamiltonian cycles in hypergraphs with dense link graphs

Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs

High powers of Hamiltonian cycles in randomly augmented graphs

Andrásfai and Vega graphs in Ramsey-Turán theory

Minimum pair degree condition for tight Hamiltonian cycles in $4$ -uniform hypergraphs