Geodesic
On the Circumference of Essentially 4-connected Planar Graphs
Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 1, pp. 21-46.

Voir la notice de l'article provenant de la source Journal of Graph Algorythms and Applications website

A planar graph is essentially 4-connected if it is 3-connected and every of its 3-separators is the neighborhood of a single vertex. Jackson and Wormald proved that every essentially 4-connected planar graph G on n vertices contains a cycle of length at least 2n+45, and this result has recently been improved multiple times. In this paper, we prove that every essentially 4-connected planar graph G on n vertices contains a cycle of length at least 58(n+2). This improves the previously best-known lower bound 35(n+2).
DOI : 10.7155/jgaa.00516
Mots-clés : Circumference, Essentially 4-Connected Planar Graphs, Longest Cycle, Discharging, Tutte Cycle 
@article{JGAA_2020_24_1_a1,
     author = {Igor Fabrici and Jochen Harant and Samuel Mohr and Jens Schmidt},
     title = {On the {Circumference} of {Essentially} 4-connected {Planar} {Graphs}},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {21--46},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2020},
     doi = {10.7155/jgaa.00516},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.7155/jgaa.00516/}
}
TY  - JOUR
AU  - Igor Fabrici
AU  - Jochen Harant
AU  - Samuel Mohr
AU  - Jens Schmidt
TI  - On the Circumference of Essentially 4-connected Planar Graphs
JO  - Journal of Graph Algorithms and Applications
PY  - 2020
SP  - 21
EP  - 46
VL  - 24
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.7155/jgaa.00516/
DO  - 10.7155/jgaa.00516
LA  - en
ID  - JGAA_2020_24_1_a1
ER  - 
%0 Journal Article
%A Igor Fabrici
%A Jochen Harant
%A Samuel Mohr
%A Jens Schmidt
%T On the Circumference of Essentially 4-connected Planar Graphs
%J Journal of Graph Algorithms and Applications
%D 2020
%P 21-46
%V 24
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.7155/jgaa.00516/
%R 10.7155/jgaa.00516
%G en
%F JGAA_2020_24_1_a1
Igor Fabrici; Jochen Harant; Samuel Mohr; Jens Schmidt. On the Circumference of Essentially 4-connected Planar Graphs. Journal of Graph Algorithms and Applications, Tome 24 (2020) no. 1, pp. 21-46. doi : 10.7155/jgaa.00516. https://geodesic-test.mathdoc.fr/articles/10.7155/jgaa.00516/

Cité par Sources :