In this paper, we develop a new rainbow Hamilton framework, which is of independent
interest, settling the problem proposed by Gupta, Hamann, M\"{u} yesser, Parczyk, and …

We study the following rainbow version of subgraph containment problems in a family of
(hyper) graphs, which generalizes the classical subgraph containment problems in a single …

A famous theorem of Dirac states that any graph on n vertices with minimum degree at least
n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we …

We study approximate decompositions of edge‐colored quasirandom graphs into rainbow
spanning structures: an edge‐coloring of a graph is locally‐bounded if every vertex is …

We prove a rainbow version of the blow‐up lemma of Komlós, Sárközy, and Szemerédi for
μn‐bounded edge colorings. This enables the systematic study of rainbow embeddings of …

An n-queens configuration is a placement of n mutually non-attacking queens on an n× n
chessboard. The n-queens completion problem, introduced by Nauck in 1850, is to decide …

A tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the
vertices of G such that every set of k consecutive vertices in the ordering forms an edge …

We prove that for fixed $ r\ge k\ge 2$, every $ k $-uniform hypergraph on $ n $ vertices
having minimum codegree at least $(1-(\binom {r-1}{k-1}+\binom {r-2}{k-2})^{-1}) n+ o (n) …

We study the following rainbow version of subgraph containment problems in a family of
(hyper) graphs, which generalizes the classical subgraph containment problems in a single …

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours.
The study of rainbow subgraphs goes back to the work of Euler on Latin squares. This article …