# 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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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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