DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 20(1) (2000) 105-107
DOI: https://doi.org/10.7151/dmgt.1110

LONG INDUCED PATHS IN 3-CONNECTED PLANAR GRAPHS

Jorge Luis Arocha and Pilar Valencia

Instituto de Matemáticas, UNAM, Ciudad Universitaria
Area de la Investigación Científica, Circuito Exterior
México, D.F. 04510
e-mail: arocha@math.unam.mx

e-mail: pilarvalencia@hotmail.com

Abstract

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.

1991 Mathematics Subject Classification: 05C38, 05C40.

References

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[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)22:1<23::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.
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Received 22 June 1999
Revised 1 October 1999


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