Geodesic
A different short proof of Brook's theorem
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 633-634.

Voir la notice de l'article provenant de la source Library of Science

Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.
Keywords: coloring, clique number, maximum degree 
@article{DMGT_2014_34_3_a15,
     author = {Rabern, Landon},
     title = {A different short proof of {Brook's} theorem},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {633--634},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a15/}
}
TY  - JOUR
AU  - Rabern, Landon
TI  - A different short proof of Brook's theorem
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 633
EP  - 634
VL  - 34
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a15/
LA  - en
ID  - DMGT_2014_34_3_a15
ER  - 
%0 Journal Article
%A Rabern, Landon
%T A different short proof of Brook's theorem
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 633-634
%V 34
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a15/
%G en
%F DMGT_2014_34_3_a15
Rabern, Landon. A different short proof of Brook's theorem. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 633-634. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a15/

[1] R.L. Brooks, On colouring the nodes of a network, in: Math. Proc. Cambridge Philos. Soc. 37 Cambridge Univ. Press (1941) 194-197.

[2] R. Diestel, Graph Theory (Fourth Ed., Springer Verlag, 2010).

[3] A.D. King, Hitting all maximum cliques with a stable set using lopsided independent transversals, J. Graph Theory 67 (2011) 300-305. doi:10.1002/jgt.20532

[4] A.V. Kostochka, Degree, density, and chromatic number, Metody Diskret. Anal. 35 (1980) 45-70 (in Russian).

[5] L. Lovász, Three short proofs in graph theory, J. Combin. Theory (B) 19 (1975) 269-271. doi:10.1016/0095-8956(75)90089-1

[6] L. Rabern, On hitting all maximum cliques with an independent set, J. Graph Theory 66 (2011) 32-37. doi:10.1002/jgt.20487

[7] H. Tverberg, On Brooks’ theorem and some related results, Math. Scand. 52 (1983) 37-40.