On degrees of vertices in paradoxical trees

W. A. Deuber; A. V. Kostochka

doi:10.1016/S0012-365X(99)00208-3

On degrees of vertices in paradoxical trees

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

Abstract

We present some necessary and sufficient conditions (in terms of degrees of vertices) for locally finite tree T=(V,E) to be paradoxical, i.e. to have a partition V=V₁∪V₂ and one-to-one mappings f_i : V → Vi, i=1,2 such that the supremum of the distances between v and f_i(v) over v ∈ V and i = 1,2 is finite.

Original language	English (US)
Pages (from-to)	53-59
Number of pages	7
Journal	Discrete Mathematics
Volume	212
Issue number	1-2
DOIs	https://doi.org/10.1016/S0012-365X(99)00208-3
State	Published - Feb 6 2000
Externally published	Yes

Keywords

Locally finite trees
Vertex degrees

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Online availability

10.1016/S0012-365X(99)00208-3

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AU - Kostochka, A. V.

PY - 2000/2/6

Y1 - 2000/2/6

N2 - We present some necessary and sufficient conditions (in terms of degrees of vertices) for locally finite tree T=(V,E) to be paradoxical, i.e. to have a partition V=V1∪V2 and one-to-one mappings fi : V → Vi, i=1,2 such that the supremum of the distances between v and fi(v) over v ∈ V and i = 1,2 is finite.

AB - We present some necessary and sufficient conditions (in terms of degrees of vertices) for locally finite tree T=(V,E) to be paradoxical, i.e. to have a partition V=V1∪V2 and one-to-one mappings fi : V → Vi, i=1,2 such that the supremum of the distances between v and fi(v) over v ∈ V and i = 1,2 is finite.

KW - Locally finite trees

KW - Vertex degrees

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JF - Discrete Mathematics

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On degrees of vertices in paradoxical trees

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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