Triangle-free planar graphs with minimum degree 3 have radius at least 3

Seog-Jin Kim; Douglas B. West

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 3, page 563-566
  • ISSN: 2083-5892

Abstract

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We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.

How to cite

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Seog-Jin Kim, and Douglas B. West. "Triangle-free planar graphs with minimum degree 3 have radius at least 3." Discussiones Mathematicae Graph Theory 28.3 (2008): 563-566. <http://eudml.org/doc/270244>.

@article{Seog2008,
abstract = {We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.},
author = {Seog-Jin Kim, Douglas B. West},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {planar graph; radius; minimum degree; triangle-free; dominating set},
language = {eng},
number = {3},
pages = {563-566},
title = {Triangle-free planar graphs with minimum degree 3 have radius at least 3},
url = {http://eudml.org/doc/270244},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Seog-Jin Kim
AU - Douglas B. West
TI - Triangle-free planar graphs with minimum degree 3 have radius at least 3
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 3
SP - 563
EP - 566
AB - We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.
LA - eng
KW - planar graph; radius; minimum degree; triangle-free; dominating set
UR - http://eudml.org/doc/270244
ER -

References

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  1. [1] P. Erdös, J. Pach, R. Pollack and Zs. Tuza, Radius, diameter, and minimum degree, J. Combin. Theory (B) 47 (1989) 73-79, doi: 10.1016/0095-8956(89)90066-X. 
  2. [2] J. Harant, An upper bound for the radius of a 3-connected planar graph with bounded faces, Contemporary methods in graph theory (Bibliographisches Inst., Mannheim, 1990), 353-358. 
  3. [3] J. Plesník, Critical graphs of given diameter, Acta Fac. Rerum Natur. Univ. Comenian. Math. 30 (1975) 71-93. Zbl0318.05115

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