JGT
2007
13 years 11 months ago
2007
A well-known theorem of Mader [5] states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. Solving a problem of Diestel [2], we ex...
JGT
2007
13 years 11 months ago
2007
Let Γ be an infinite, locally finite, connected graph with distance function δ. Given a ray P in Γ and a constant C ≥ 1, a vertex-sequence {xn}∞ n=0 ⊆ V P is said to be...
JGT
2007
13 years 11 months ago
2007
JGT
2007
13 years 11 months ago
2007
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This im...