On chromaticity of graphs

• Autorzy: Ewa Łazuka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

chromatic polynomial; chromatically equivalent graphs; chromatic characterization

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 19-31

Daty

wydano

1995

otrzymano

1994-02-17

poprawiono

1994-07-09

Twórcy

autor

Ewa Łazuka

• 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.

Identyfikatory

DOI

10.7151/dmgt.1003