## Abstract In this paper we obtain chromatic polynomials of connected 3β and 4βchromatic planar graphs that are maximal for positive integerβvalued arguments. We also characterize the class of connected 3βchromatic graphs having the maximum number of __p__βcolorings for __p__ β₯ 3, thus extending a
Chromatic polynomials of connected graphs
β Scribed by Chong-Yun Chao; Lian-Chang Zhao
- Book ID
- 112496117
- Publisher
- Springer
- Year
- 1984
- Tongue
- English
- Weight
- 276 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
## Abstract In this paper we obtain chromatic polynomials __P(G__; Ξ») of 2βconnected graphs of order __n__ that are maximum for positive integerβvalued arguments Ξ» β§ 3. The extremal graphs are cycles __C__~__n__~ and these graphs are unique for every Ξ» β§ 3 and __n__ β 5. We also determine max{__P(
## Abstract In the set of graphs of order __n__ and chromatic number __k__ the following partial order relation is defined. One says that a graph __G__ is less than a graph __H__ if __c__~__i__~(__G__) β€ __c__~__i__~(__H__) holds for every __i__, __k__ β€ __i__ β€ __n__ and at least one inequality is
Let G be a graph of order n, maximum degree , and minimum degree . Let P(G, ) be the chromatic polynomial of G. It is known that the multiplicity of zero "0" of P(G, ) is one if G is connected, and the multiplicity of zero "1" of P(G, ) is one if G is 2-connected. Is the multiplicity of zero "2" of