The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six

Halina Bielak

Discussiones Mathematicae Graph Theory (1998)

  • Volume: 18, Issue: 1, page 99-111
  • ISSN: 2083-5892

Abstract

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In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.

How to cite

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Halina Bielak. "The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six." Discussiones Mathematicae Graph Theory 18.1 (1998): 99-111. <http://eudml.org/doc/270193>.

@article{HalinaBielak1998,
abstract = {In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.},
author = {Halina Bielak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {chromatically equivalent graphs; chromatic polynomial; chromatically unique graphs; cyclomatic number; chromatic equivalence; chromatic number; chromaticity},
language = {eng},
number = {1},
pages = {99-111},
title = {The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six},
url = {http://eudml.org/doc/270193},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Halina Bielak
TI - The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six
JO - Discussiones Mathematicae Graph Theory
PY - 1998
VL - 18
IS - 1
SP - 99
EP - 111
AB - In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.
LA - eng
KW - chromatically equivalent graphs; chromatic polynomial; chromatically unique graphs; cyclomatic number; chromatic equivalence; chromatic number; chromaticity
UR - http://eudml.org/doc/270193
ER -

References

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  1. [1] C.Y. Chao and E.G. Whitehead Jr., Chromatically unique graphs, Discrete Math. 27 (1979) 171-177, doi: 10.1016/0012-365X(79)90107-9. Zbl0411.05035
  2. [2] K.M. Koh and C.P. Teo, The search for chromatically unique graphs, Graphs and Combinatorics 6 (1990) 259-285, doi: 10.1007/BF01787578. Zbl0727.05023
  3. [3] K.M. Koh and C.P. Teo, The chromatic uniqueness of certain broken wheels, Discrete Math. 96 (1991) 65-69, doi: 10.1016/0012-365X(91)90471-D. Zbl0752.05029
  4. [4] F. Harary, Graph Theory (Reading, 1969). 
  5. [5] N-Z. Li and E.G. Whitehead Jr., The chromaticity of certain graphs with five triangles, Discrete Math. 122 (1993) 365-372, doi: 10.1016/0012-365X(93)90312-H. Zbl0787.05040
  6. [6] 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

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