# vertex-transitive

## Matching polynomials of vertex transitive graphs ★★

Author(s): Mohar

\begin{conjecture} For every integer $r$ there exists a vertex transitive graph $G$ whose matching polynomial has a root of multiplicity at least $r$. \end{conjecture}

Keywords: matching polynomial; vertex-transitive

## Hamiltonian paths and cycles in vertex transitive graphs ★★★

Author(s): Lovasz

\begin{problem} Does every connected \Def{vertex-transitive graph} have a \Def{Hamiltonian path}? \end{problem}

Keywords: cycle; hamiltonian; path; vertex-transitive