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

• Autorzy: Halina Bielak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

chromatically equivalent graphs; chromatic polynomial; chromatically unique graphs; cyclomatic number

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1998
• Tom: 18
• Numer: 1
• Strony: 99-111

Daty

wydano

1998

otrzymano

1997-05-25

poprawiono

1997-09-16

Twórcy

autor

Halina Bielak

• Institute of Mathematics, M. Curie-Skłodowska University, Lublin, Poland

Bibliografia

• [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.
• [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.
• [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.
• [4] F. Harary, Graph Theory (Reading, 1969).
• [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.
• [6] R.C. Read, An introduction to chromatic polynomials, J. Combin. Theory 4 (1968) 52-71, doi: 10.1016/S0021-9800(68)80087-0.

Identyfikatory

DOI

10.7151/dmgt.1067