From One to Many Rainbow Hamiltonian Cycles

@article{Bradshaw2021FromOT,
title={From One to Many Rainbow Hamiltonian Cycles},
journal={Graphs and Combinatorics},
year={2021},
volume={38}
}
• Published 14 April 2021
• Materials Science
• Graphs and Combinatorics
Given a graph G and a family G={G1,…,Gn}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G} = \{G_1,\ldots ,G_n\}$$\end{document} of subgraphs of G, a transversal of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy…
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References

SHOWING 1-10 OF 36 REFERENCES

Additive triples of bijections, or the toroidal semiqueens problem

• Mathematics
Journal of the European Mathematical Society
• 2018

Representation of Large Matchings in Bipartite Graphs

• Mathematics
SIAM J. Discret. Math.
• 2017
It is shown that the $o(n)$ term can be reduced to a constant, namely $f (n) \le \lceil \frac{3}{2}n \rceil+1$.

A rainbow version of Mantel's Theorem

• Mathematics
• 2020
Mantel's Theorem from 1907 is one of the oldest results in graph theory: every simple $n$-vertex graph with more than $\frac{1}{4}n^2$ edges contains a triangle. The theorem has been generalized in

Vertex Degree Sums for Perfect Matchings in 3-Uniform Hypergraphs

• Mathematics
Electron. J. Comb.
• 2018
The minimum degree sum of two adjacent vertices that ensures a perfect matching in a 3-uniform hypergraph without an isolated vertex is determined and the (unique) extremal hyergraph is a different space barrier from the one for the corresponding Dirac problem.

• Mathematics
• 2022

Hamiltonian cycles in Dirac graphs

• Mathematics
Comb.
• 2009
It is proved that for any n-vertex Dirac graph G=(V,E), the number, Ψ(G), of Hamiltonian cycles in G is at least exp_2, where h(G) =maxΣexe log(1/xe), the maximum over x: E → ℜ+ satisfying Σe∋υxe = 1 for each υ ∈ V, and log =log2.

On a rainbow version of Dirac's theorem

• Mathematics
Bulletin of the London Mathematical Society
• 2020
For a collection G={G1,⋯,Gs} of not necessarily distinct graphs on the same vertex set V , a graph H with vertices in V is a G ‐transversal if there exists a bijection ϕ:E(H)→[s] such that e∈E(Gϕ(e))

Regular Graphs with Few Longest Cycles

Motivated by work of Haythorpe, Thomassen and the author showed that there exists a positive constant c such that there is an infinite family of 4-regular 4-connected graphs, each containing exactly