Geodesic
BROOKS’ THEOREM FOR MEASURABLE COLORINGS
Forum of Mathematics, Sigma, Tome 4 (2016)

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

We generalize Brooks’ theorem to show that if $G$ is a Borel graph on a standard Borel space $X$ of degree bounded by $d\geqslant 3$ which contains no $(d+1)$ -cliques, then $G$ admits a ${\it\mu}$ -measurable $d$ -coloring with respect to any Borel probability measure ${\it\mu}$ on $X$ , and a Baire measurable $d$ -coloring with respect to any compatible Polish topology on $X$ . The proof of this theorem uses a new technique for constructing one-ended spanning subforests of Borel graphs, as well as ideas from the study of list colorings. We apply the theorem to graphs arising from group actions to obtain factor of IID $d$ -colorings of Cayley graphs of degree $d$ , except in two exceptional cases. 
@article{10_1017_fms_2016_14,
     author = {CLINTON T. CONLEY and ANDREW S. MARKS and ROBIN D. TUCKER-DROB},
     title = {BROOKS{\textquoteright} {THEOREM} {FOR} {MEASURABLE} {COLORINGS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {4},
     year = {2016},
     doi = {10.1017/fms.2016.14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.14/}
}
TY  - JOUR
AU  - CLINTON T. CONLEY
AU  - ANDREW S. MARKS
AU  - ROBIN D. TUCKER-DROB
TI  - BROOKS’ THEOREM FOR MEASURABLE COLORINGS
JO  - Forum of Mathematics, Sigma
PY  - 2016
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.14/
DO  - 10.1017/fms.2016.14
LA  - en
ID  - 10_1017_fms_2016_14
ER  - 
%0 Journal Article
%A CLINTON T. CONLEY
%A ANDREW S. MARKS
%A ROBIN D. TUCKER-DROB
%T BROOKS’ THEOREM FOR MEASURABLE COLORINGS
%J Forum of Mathematics, Sigma
%D 2016
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.14/
%R 10.1017/fms.2016.14
%G en
%F 10_1017_fms_2016_14
CLINTON T. CONLEY; ANDREW S. MARKS; ROBIN D. TUCKER-DROB. BROOKS’ THEOREM FOR MEASURABLE COLORINGS. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2016.14

Cité par Sources :