Geodesic
Triangle-free planar graphs with minimum degree 3 have radius at least 3
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 563-566.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: planar graph, radius, minimum degree, triangle-free, dominating set 
@article{DMGT_2008_28_3_a14,
     author = {Kim, Seog-Jim and West, Douglas},
     title = {Triangle-free planar graphs with minimum degree 3 have radius at least 3},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {563--566},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a14/}
}
TY  - JOUR
AU  - Kim, Seog-Jim
AU  - West, Douglas
TI  - Triangle-free planar graphs with minimum degree 3 have radius at least 3
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2008
SP  - 563
EP  - 566
VL  - 28
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a14/
LA  - en
ID  - DMGT_2008_28_3_a14
ER  - 
%0 Journal Article
%A Kim, Seog-Jim
%A West, Douglas
%T Triangle-free planar graphs with minimum degree 3 have radius at least 3
%J Discussiones Mathematicae. Graph Theory
%D 2008
%P 563-566
%V 28
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a14/
%G en
%F DMGT_2008_28_3_a14
Kim, Seog-Jim; West, Douglas. Triangle-free planar graphs with minimum degree 3 have radius at least 3. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 563-566. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a14/

[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.