Trees Through Specified Vertices
We prove a conjecture of Horak that can be thought of as an extension of classical results including Dirac's theorem on the existence of Hamiltonian cycles. Namely, we prove for 1 ≤ k ≤ n - 2 if G is a connected graph with A ⊂ V (G) such that dG (v) ≥ k for all v ∈ A, then there exists a subtree T of G such that V (T) ⊃ A and dT (v) ≤ ⌈ frac(n - 1, k) ⌉ for all v ∈ A.
MSU Digital Commons Citation
Cutler, Jonathan, "Trees Through Specified Vertices" (2009). Department of Mathematics Facuty Scholarship and Creative Works. 185.