An inductive proof of Whitney's Broken Circuit Theorem

Klaus Dohmen

Discussiones Mathematicae Graph Theory (2011)

  • Volume: 31, Issue: 3, page 509-515
  • ISSN: 2083-5892

Abstract

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

How to cite

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Klaus Dohmen. "An inductive proof of Whitney's Broken Circuit Theorem." Discussiones Mathematicae Graph Theory 31.3 (2011): 509-515. <http://eudml.org/doc/270937>.

@article{KlausDohmen2011,
abstract = {We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.},
author = {Klaus Dohmen},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {chromatic polynomial; broken circuit; induction},
language = {eng},
number = {3},
pages = {509-515},
title = {An inductive proof of Whitney's Broken Circuit Theorem},
url = {http://eudml.org/doc/270937},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Klaus Dohmen
TI - An inductive proof of Whitney's Broken Circuit Theorem
JO - Discussiones Mathematicae Graph Theory
PY - 2011
VL - 31
IS - 3
SP - 509
EP - 515
AB - We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.
LA - eng
KW - chromatic polynomial; broken circuit; induction
UR - http://eudml.org/doc/270937
ER -

References

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  1. [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. Zbl43.0574.02
  2. [2] N. Biggs, Algebraic Graph Theory, 2nd edition, (Cambridge University Press, 1994). Zbl0797.05032
  3. [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. Zbl0592.05022
  4. [4] K. Dohmen, An improvement of the inclusion-exclusion principle, Arch. Math. 72 (1999) 298-303, doi: 10.1007/s000130050336. Zbl0934.05011
  5. [5] R.C. Read, An introduction to chromatic polynomials, J. Combin. Theory 4 (1968) 52-71, doi: 10.1016/S0021-9800(68)80087-0. Zbl0173.26203
  6. [6] H. Whitney, A logical expansion in mathematics, Bull. Amer. Math. Soc. 38 (1932) 572-579, doi: 10.1090/S0002-9904-1932-05460-X. Zbl0005.14602

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