Displaying similar documents to “Star Coloring of Subcubic Graphs”

Uniformly convex functions II

Wancang Ma, David Minda (1993)

Annales Polonici Mathematici

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Recently, A. W. Goodman introduced the class UCV of normalized uniformly convex functions. We present some sharp coefficient bounds for functions f(z) = z + a₂z² + a₃z³ + ... ∈ UCV and their inverses f - 1 ( w ) = w + d ₂ w ² + d ₃ w ³ + . . . . The series expansion for f - 1 ( w ) converges when | w | < ϱ f , where 0 < ϱ f depends on f. The sharp bounds on | a n | and all extremal functions were known for n = 2 and 3; the extremal functions consist of a certain function k ∈ UCV and its rotations. We obtain the sharp bounds on | a n | and all extremal functions for...

On potentially H -graphic sequences

Meng Xiao Yin, Jian Hua Yin (2007)

Czechoslovak Mathematical Journal

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For given a graph H , a graphic sequence π = ( d 1 , d 2 , ... , d n ) is said to be potentially H -graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially ( K 5 - e ) -positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K 5 -graphic, where K r is a complete graph on r vertices and K r - e is a graph obtained from K r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition...