Du, Q., On o-polynomials and a class of chromatically unique graphs, Discrete Mathematics 115 (1993) 153-165. Let cr(G)=C:,,aicr '-' be the u-polynomial of a graph G. We ask the question: When k and a, are given, what is the largest possible value of ai(O < i < k) for any graph G? In this paper, thi
A characterization of chromatically rigid polynomials
β Scribed by O. V. Vorodin; I. G. Dmitriev
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1991
- Tongue
- English
- Weight
- 486 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0037-4466
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π SIMILAR VOLUMES
A polynomial in two variables is defned by C,(x,t)= ~-~cn,, Z( a~,x)tl~l, where Hn is the lattice of partitions of the set { I, 2 ..... n}, G~ is a certain interval graph defined in terms of the partition 7r, z(G~,x) is the chromatic polynomial of G~ and Inl is the number of blocks in n. It " t ~-~i
Frucht and Giudici classified all graphs having quadratic a-polynomials. Here w e classify all chromatically unique graphs having quadratic (Tpolynomials.
Let P(G, \*) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number \* n, (\*&2) n&1 P(G, \*)&\*(\*&1) n&2 P(G, \*&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1))
In this paper it is proved that if the chromatic polynomial P(G; 2) is maximum for 2 = 3 in the class of 3-chromatic 2-connected graphs G of order n, then G is isomorphic to the graph consisting of C4 and Cn-l, having in common a path of length two for every even n/> 6. This solves a conjecture rais