Powers of Hamiltonian cycles in multipartite graphs

@article{DeBiasio2022PowersOH,
  title={Powers of Hamiltonian cycles in multipartite graphs},
  author={Louis DeBiasio and Ryan R. Martin and Theodore Molla},
  journal={Discret. Math.},
  year={2022},
  volume={345},
  pages={112747}
}

Figures from this paper

References

SHOWING 1-10 OF 30 REFERENCES
On extremal problems of graphs and generalized graphs
TLDR
It is proved that to everyl andr there is anε(l, r) so that forn>n0 everyr-graph ofn vertices andnr−ε( l, r), which means that all ther-tuples occur in ther-graph.
Proof of a conjecture of P. Erdös on the derivative of a polynomial
Introduction. We start out from the following consequence of S. Bernstein's well known theorem on trigonometric polynomials. Let pn(z) be a polynomial of degree n for which | ^(^) | ^ 1 holds as \z\
Proof of the Seymour conjecture for large graphs
Paul Seymour conjectured that any graphG of ordern and minimum degree of at leastk/k+1n contains thekth power of a Hamiltonian cycle. Here, we prove this conjecture for sufficiently largen.
Asymptotic multipartite version of the Alon-Yuster theorem
Tripartite version of the Corrádi-Hajnal theorem
An asymptotic bound for the strong chromatic number
TLDR
It is shown that for every c > 0 and every graph G on n vertices with Δ(G) ≥ cn, χs (G) ≤ (2+o(1)))Δ(G), which is asymptotically best possible.
Factors of r-partite graphs and bounds for the Strong Chromatic Number
We give an optimal degree condition for a tripartite graph to have a spanning subgraph consisting of complete graphs of order 3. This result is used to give an upper bound of 2 Delta for the strong
A multipartite Hajnal-Szemerédi theorem
A Geometric Theory for Hypergraph Matching
We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two
A Multipartite Version of the Hajnal–Szemerédi Theorem for Graphs and Hypergraphs
TLDR
It is shown that, for any γ > 0, if every vertex x ∈ Vi is joined to at least $\bigl ((t-1)/t + \gamma \bigr )n$ vertices of Vj for each j ≠ i, then G contains a perfect Kt-matching, provided n is large enough.
...
...