Geodesic
COLORING CURVES ON SURFACES
Forum of Mathematics, Sigma, Tome 6 (2018)

Voir la notice de l'article provenant de la source Cambridge University Press

We study the chromatic number of the curve graph of a surface. We show that the chromatic number grows like $k\log k$ for the graph of separating curves on a surface of Euler characteristic $-k$. We also show that the graph of curves that represent a fixed nonzero homology class is uniquely $t$-colorable, where $t$ denotes its clique number. Together, these results lead to the best known bounds on the chromatic number of the curve graph. We also study variations for arc graphs and obtain exact results for surfaces of low complexity. Our investigation leads to connections with Kneser graphs, the Johnson homomorphism, and hyperbolic geometry. 
@article{10_1017_fms_2018_12,
     author = {JONAH GASTER and JOSHUA EVAN GREENE and NICHOLAS G. VLAMIS},
     title = {COLORING {CURVES} {ON} {SURFACES}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {6},
     year = {2018},
     doi = {10.1017/fms.2018.12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.12/}
}
TY  - JOUR
AU  - JONAH GASTER
AU  - JOSHUA EVAN GREENE
AU  - NICHOLAS G. VLAMIS
TI  - COLORING CURVES ON SURFACES
JO  - Forum of Mathematics, Sigma
PY  - 2018
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.12/
DO  - 10.1017/fms.2018.12
LA  - en
ID  - 10_1017_fms_2018_12
ER  - 
%0 Journal Article
%A JONAH GASTER
%A JOSHUA EVAN GREENE
%A NICHOLAS G. VLAMIS
%T COLORING CURVES ON SURFACES
%J Forum of Mathematics, Sigma
%D 2018
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.12/
%R 10.1017/fms.2018.12
%G en
%F 10_1017_fms_2018_12
JONAH GASTER; JOSHUA EVAN GREENE; NICHOLAS G. VLAMIS. COLORING CURVES ON SURFACES. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.12

Cité par Sources :