: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth...
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...
Penny E. Haxell, Ben Seamone, Jacques Verstraë...
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...
C. Paul Bonnington, R. Bruce Richter, Mark E. Watk...