An inductive proof of Whitney's Broken Circuit Theorem
Klaus Dohmen
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 509-515 / Harvested from The Polish Digital Mathematics Library

We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:270937
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     title = {An inductive proof of Whitney's Broken Circuit Theorem},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {31},
     year = {2011},
     pages = {509-515},
     zbl = {1229.05102},
     language = {en},
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Klaus Dohmen. An inductive proof of Whitney's Broken Circuit Theorem. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 509-515. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1561/

[000] [1] G.D. Birkhoff, A determinant formula for the number of ways of coloring a map, Ann. Math. 14 (1912) 42-46, doi: 10.2307/1967597. | Zbl 43.0574.02

[001] [2] N. Biggs, Algebraic Graph Theory, 2nd edition, (Cambridge University Press, 1994). | Zbl 0797.05032

[002] [3] A. Blass and B.E. Sagan, Bijective proofs of two broken circuit theorems, J. Graph Theory 10 (1986) 15-21, doi: 10.1002/jgt.3190100104. | Zbl 0592.05022

[003] [4] K. Dohmen, An improvement of the inclusion-exclusion principle, Arch. Math. 72 (1999) 298-303, doi: 10.1007/s000130050336. | Zbl 0934.05011

[004] [5] R.C. Read, An introduction to chromatic polynomials, J. Combin. Theory 4 (1968) 52-71, doi: 10.1016/S0021-9800(68)80087-0. | Zbl 0173.26203

[005] [6] H. Whitney, A logical expansion in mathematics, Bull. Amer. Math. Soc. 38 (1932) 572-579, doi: 10.1090/S0002-9904-1932-05460-X. | Zbl 0005.14602