A Different Short Proof of Brooks’ Theorem
Discussiones Mathematicae Graph Theory (2014)
- Volume: 34, Issue: 3, page 633-634
- ISSN: 2083-5892
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Abstract
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topLandon Rabern. "A Different Short Proof of Brooks’ Theorem." Discussiones Mathematicae Graph Theory 34.3 (2014): 633-634. <http://eudml.org/doc/267828>.
@article{LandonRabern2014,
abstract = {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.},
author = {Landon Rabern},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {coloring; clique number; maximum degree},
language = {eng},
number = {3},
pages = {633-634},
title = {A Different Short Proof of Brooks’ Theorem},
url = {http://eudml.org/doc/267828},
volume = {34},
year = {2014},
}
TY - JOUR
AU - Landon Rabern
TI - A Different Short Proof of Brooks’ Theorem
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 3
SP - 633
EP - 634
AB - 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.
LA - eng
KW - coloring; clique number; maximum degree
UR - http://eudml.org/doc/267828
ER -
References
top- [1] R.L. Brooks, On colouring the nodes of a network, in: Math. Proc. Cambridge Philos. Soc. 37 Cambridge Univ. Press (1941) 194-197. Zbl0027.26403
- [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[WoS][Crossref] Zbl1231.05205
- [4] A.V. Kostochka, Degree, density, and chromatic number, Metody Diskret. Anal. 35 (1980) 45-70 (in Russian).
- [5] L. Lov´asz, Three short proofs in graph theory, J. Combin. Theory (B) 19 (1975) 269-271. doi:10.1016/0095-8956(75)90089-1[Crossref]
- [6] L. Rabern, On hitting all maximum cliques with an independent set, J. Graph Theory 66 (2011) 32-37. doi:10.1002/jgt.20487[Crossref][WoS] Zbl1222.05201
- [7] H. Tverberg, On Brooks’ theorem and some related results, Math. Scand. 52 (1983) 37-40. Zbl0512.05028
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