English

Subcubic planar graphs of girth 7 are class I

Combinatorics 2022-04-25 v2 Discrete Mathematics
Authors: Sebastien Bonduelle , František Kardoš
View on arXiv ↗ PDF ↗

Abstract

We prove that planar graphs of maximum degree 3 and of girth at least 7 are 3-edge-colorable, extending the previous result for girth at least 8 by Kronk, Radlowski, and Franen from 1974.

Keywords

graph coloring graph theory

Cite

@article{arxiv.2108.06115,
  title  = {Subcubic planar graphs of girth 7 are class I},
  author = {Sebastien Bonduelle and František Kardoš},
  journal= {arXiv preprint arXiv:2108.06115},
  year   = {2022}
}

Comments

7 pages plus 6 pages of annex; 11 figures

Related papers

View all related →
Combinatorics · Mathematics
Planar graphs with girth at least 5 are (3,4)-colorable
Ilkyoo Choi, Gexin Yu, Xia Zhang
2019-08-09
Combinatorics · Mathematics
The chromatic number of the square of subcubic planar graphs
Stephen G. Hartke, Sogol Jahanbekam, Brent Thomas
2016-04-25
Combinatorics · Mathematics
Strong edge coloring of planar graphs
Dávid Hudák, Borut Lužar, Roman Soták, Riste Škrekovski
2014-02-24
Discrete Mathematics · Computer Science
List coloring the square of sparse graphs with large degree
Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou
2013-08-21
Combinatorics · Mathematics
Note on 3-Choosability of Planar Graphs with Maximum Degree 4
François Dross, Borut Lužar, Mária Maceková, Roman Soták
2020-05-15
Combinatorics · Mathematics
Density of $3$-critical signed graphs
Laurent Beaudou, Penny Haxell, Kathryn Nurse, Sagnik Sen +1
2023-09-11
Discrete Mathematics · Computer Science
1-planar graphs with minimum degree at least 3 have bounded girth
François Dross
2020-01-17
Discrete Mathematics · Computer Science
Strong edge-colouring of sparse planar graphs
Julien Bensmail, Ararat Harutyunyan, Hervé Hocquard, Petru Valicov
2014-07-22
Combinatorics · Mathematics
Graphs with girth $2\ell+1$ and without longer odd holes are $3$-colorable
Rong Chen
2023-01-03
Combinatorics · Mathematics
Circular edge-colorings of cubic graphs with girth six
D. Král', E. Mácajová, J. Mazák, J. -S. Sereni
2010-05-28
Combinatorics · Mathematics
Light edges in 1-planar graphs of minimum degree 3
Bei Niu, Xin Zhang
2019-12-17
Combinatorics · Mathematics
Class two 1-planar graphs with maximum degree six or seven
Xin Zhang
2011-04-26
Combinatorics · Mathematics
Graphs with girth 9 and without longer odd holes are 3-colorable
Yan Wang, Rong Wu
2023-07-06
Combinatorics · Mathematics
Size of edge-critical uniquely 3-colorable planar graphs
Zepeng Li, Enqiang Zhu, Zehui Shao, Jin Xu
2013-12-31
Combinatorics · Mathematics
$(1, k)$-coloring of graphs with girth at least $5$ on a surface
Hojin Choi, Ilkyoo Choi, Jisu Jeong, Geewon Suh
2014-12-02
Combinatorics · Mathematics
Graphs with large minimum degree and no small odd cycles are $3$-colourable
Julia Böttcher, Nóra Frankl, Domenico Mergoni Cecchelli, Olaf Parczyk +1
2023-03-08
Discrete Mathematics · Computer Science
Graphs with maximum degree D at least 17 and maximum average degree less than 3 are list 2-distance (D+2)-colorable
Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou
2013-01-31
Combinatorics · Mathematics
Planar graphs without 4-cycles and close triangles are (2,0,0)-colorable
Heather Hoskins, Runrun Liu, Jennifer Vandenbussche, Gexin Yu
2018-06-21
Combinatorics · Mathematics
Fractional coloring of planar graphs of girth five
Zdeněk Dvořák, Xiaolan Hu
2018-09-17
Combinatorics · Mathematics
Improper coloring of graphs on surfaces
Ilkyoo Choi, Louis Esperet
2019-03-18
Combinatorics · Mathematics
3 List Coloring Graphs of Girth at least Five on Surfaces
Luke Postle
2017-10-20
Combinatorics · Mathematics
Planar Graphs of Girth at least Five are Square $(\Delta + 2)$-Choosable
Marthe Bonamy, Daniel W. Cranston, Luke Postle
2019-11-18
Combinatorics · Mathematics
Graphs with girth 8 and without longer even holes are 3-colorable
Yan Wang, Rong Wu
2026-05-28
Discrete Mathematics · Computer Science
Planar graphs with maximum degree D at least 8 are (D+1)-edge-choosable
Marthe Bonamy
2013-03-19
Combinatorics · Mathematics
Graphs with girth $2\ell$ and without longer even holes are $3$-colorable
Rong Chen
2025-09-03
R2 v1 2026-06-24T05:05:21.547Z