On chromaticity of graphs

Ewa Łazuka

Discussiones Mathematicae Graph Theory (1995)

  • Volume: 15, Issue: 1, page 19-31
  • ISSN: 2083-5892

Abstract

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In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.

How to cite

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Ewa Łazuka. "On chromaticity of graphs." Discussiones Mathematicae Graph Theory 15.1 (1995): 19-31. <http://eudml.org/doc/270453>.

@article{EwaŁazuka1995,
abstract = {In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.},
author = {Ewa Łazuka},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {chromatic polynomial; chromatically equivalent graphs; chromatic characterization; chromaticity; chromatic polynomials; cacti; trees; unicyclic graphs},
language = {eng},
number = {1},
pages = {19-31},
title = {On chromaticity of graphs},
url = {http://eudml.org/doc/270453},
volume = {15},
year = {1995},
}

TY - JOUR
AU - Ewa Łazuka
TI - On chromaticity of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1995
VL - 15
IS - 1
SP - 19
EP - 31
AB - In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n-gon-trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so-called clique-forest-like graphs are chromatically equivalent.
LA - eng
KW - chromatic polynomial; chromatically equivalent graphs; chromatic characterization; chromaticity; chromatic polynomials; cacti; trees; unicyclic graphs
UR - http://eudml.org/doc/270453
ER -

References

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  2. [2] C. Y. Chao and E. G. Whitehead Jr., On chromatic equivalence of graphs, in: Y. Alavi and D. R. Lick, ed., Theory and Applications of Graphs, Lecture Notes in Math. 642 (Springer, Berlin, 1978) 121-131. 
  3. [3] G. L. Chia, A note on chromatic uniqueness of graphs, J. Graph Theory 10 (1986) 541-543, doi: 10.1007/BFb0070369. Zbl0616.05035
  4. [4] B. Eisenberg, Generalized lower bounds for the chromatic polynomials, in: A. Dold and B. Eckmann, eds., Recent Trends in Graph Theory, Lecture Notes in Math. 186 (Springer, Berlin, 1971) 85-94, doi: 10.1007/BFb0059427. 
  5. [5] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969). 
  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
  7. [7] R. E. Tarjan, Depth first search and linear graph algorithms, SIAM J. Comput. 1 (1972) 146-160, doi: 10.1137/0201010. Zbl0251.05107
  8. [8] C. D. Wakelin and D. R. Woodall, Chromatic polynomials, polygon trees, and outerplanar graphs, J. Graph Theory 16 (1992) 459-466, doi: 10.1002/jgt.3190160507. Zbl0778.05074
  9. [9] 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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