Trees through specified vertices

J. Cutler

doi:10.1016/j.disc.2008.06.032

Trees through specified vertices

J. Cutler

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 d_G (v) ≥ k for all v ∈ A, then there exists a subtree T of G such that V (T) ⊃ A and d_T (v) ≤ ⌈ frac(n - 1, k) ⌉ for all v ∈ A.

Original language	English
Pages (from-to)	2749-2754
Number of pages	6
Journal	Discrete Mathematics
Volume	309
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2008.06.032
State	Published - 6 May 2009

Keywords

Subtrees through specified vertices

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10.1016/j.disc.2008.06.032

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title = "Trees through specified vertices",

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.",

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N2 - 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.

AB - 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.

KW - Subtrees through specified vertices

UR - https://www.scopus.com/pages/publications/67349272020

U2 - 10.1016/j.disc.2008.06.032

DO - 10.1016/j.disc.2008.06.032

M3 - Article

AN - SCOPUS:67349272020

SN - 0012-365X

VL - 309

SP - 2749

EP - 2754

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

ER -

Trees through specified vertices

Abstract

Keywords

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