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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.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
19-31
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-02-17
poprawiono
1994-07-09
Twórcy
autor
- Department of Applied Mathematics, Technical University of Lublin, Bernardyńska 13, 20-950 Lublin, Poland
Bibliografia
- [1] C. Y. Chao and N. Z. Li, On trees of polygons, Archiv Math. 45 (1985) 180-185, doi: 10.1007/BF01270490.
- [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] G. L. Chia, A note on chromatic uniqueness of graphs, J. Graph Theory 10 (1986) 541-543, doi: 10.1007/BFb0070369.
- [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] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
- [6] R. C. Read, An introduction to chromatic polynomials, J. Combin. Theory. 4 (1968) 52-71, doi: 10.1016/S0021-9800(68)80087-0.
- [7] R. E. Tarjan, Depth first search and linear graph algorithms, SIAM J. Comput. 1 (1972) 146-160, doi: 10.1137/0201010.
- [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.
- [9] H. Whitney, A logical expansion in mathematics, Bull. Amer. Math. Soc. 38 (1932) 572-579, doi: 10.1090/S0002-9904-1932-05460-X.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1003