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

Discussiones Mathematicae Graph Theory (2008)

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

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topSeog-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

top- [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] 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] J. Plesník, Critical graphs of given diameter, Acta Fac. Rerum Natur. Univ. Comenian. Math. 30 (1975) 71-93. Zbl0318.05115

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