Trees Through Specified Vertices

Authors

Jonathan Cutler, Montclair State UniversityFollow

Document Type

Article

Publication Date

5-6-2009

Journal / Book Title

Discrete Mathematics

Abstract

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.

Comments

This article is Open Access under an Elsevier User License.

DOI

10.1016/j.disc.2008.06.032

MSU Digital Commons Citation

Cutler, Jonathan, "Trees Through Specified Vertices" (2009). Department of Mathematics Facuty Scholarship and Creative Works. 185.
https://digitalcommons.montclair.edu/mathsci-facpubs/185

Published Citation

Cutler, J. (2009). Trees through specified vertices. Discrete mathematics, 309(9), 2749-2754.