Matching polynomials of vertex transitive graphs ★★

Author(s): Mohar

Conjecture   For every integer $ r $ there exists a vertex transitive graph $ G $ whose matching polynomial has a root of multiplicity at least $ r $.

Keywords: matching polynomial; vertex-transitive

Hamiltonian paths and cycles in vertex transitive graphs ★★★

Author(s): Lovasz

Problem   Does every connected vertex-transitive graph have a Hamiltonian path?

Keywords: cycle; hamiltonian; path; vertex-transitive

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