A Rainbow Dirac's Theorem

Abstract

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 show the existence of rainbow Hamilton cycles in $\mu n$-bounded colourings of Dirac graphs for sufficiently small $\mu >0$.

arXiv comment25 pages

References in corpus (3)

• Decompositions into spanning rainbow structures
• Properly colored and rainbow copies of graphs with few cherries
• Rainbow structures in locally bounded colourings of graphs

Cited by in corpus (3)

• On Hamiltonian Berge cycles in $3$-uniform hypergraphs
• Berge cycles in non-uniform hypergraphs
• Dirac's Theorem for hamiltonian Berge cycles in uniform hypergraphs