Geodesic
Long induced paths in 3-connected planar graphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 105-107.

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

It is shown that every 3-connected planar graph with a large number of vertices has a long induced path.
Keywords: induced paths, 3-connected planar graphs 
@article{DMGT_2000_20_1_a7,
     author = {Arocha, Jorge and Valencia, Pilar},
     title = {Long induced paths in 3-connected planar graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {105--107},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a7/}
}
TY  - JOUR
AU  - Arocha, Jorge
AU  - Valencia, Pilar
TI  - Long induced paths in 3-connected planar graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2000
SP  - 105
EP  - 107
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a7/
LA  - en
ID  - DMGT_2000_20_1_a7
ER  - 
%0 Journal Article
%A Arocha, Jorge
%A Valencia, Pilar
%T Long induced paths in 3-connected planar graphs
%J Discussiones Mathematicae. Graph Theory
%D 2000
%P 105-107
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a7/
%G en
%F DMGT_2000_20_1_a7
Arocha, Jorge; Valencia, Pilar. Long induced paths in 3-connected planar graphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 105-107. http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a7/

[1] P. Alles and S. Poljak, Long induced paths and cycles in Kneser graphs, Graphs Combin. 5 (1989) 303-306, doi: 10.1007/BF01788684.

[2] G. Bacsó and Z. Tuza, A Characterization of Graphs Without Long Induced Paths, J. Graph Theory 14 (1990) 455-464, doi: 10.1002/jgt.3190140409.

[3] F. Buckley and F. Harary, On longest induced path in graphs, Chinese Quart. J. Math. 3 (1988) 61-65.

[4] J. Dong, Some results on graphs without long induced paths, J. Graph Theory 22 (1996) 23-28, doi: 10.1002/(SICI)1097-0118(199605)22:123::AID-JGT4>3.0.CO;2-N

[5] P. Erdős, M. Saks and V. Sós, Maximum Induced Trees in Graphs, J. Combin. Theory (B) 41 (1986) 61-79, doi: 10.1016/0095-8956(86)90028-6.

[6] A. Frieze and B. Jackson, Large holes in sparse random graphs, Combinatorica 7 (1987) 265-274, doi: 10.1007/BF02579303.

[7] S. Suen, On large induced trees and long induced paths in sparse random graphs, J. Combin. Theory (B) 56 (1992) 250-262, doi: 10.1016/0095-8956(92)90021-O.