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Lower bounds and upper bounds for chromatic polynomials

Journal of Graph Theory, 1993
AbstractIn this paper we give lower bounds and upper bounds for chromatic polynomials of simple undirected graphs on n vertices having m edges and girth exceeding g © 1993 John Wiley & Sons, Inc.
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Unification, weak unification, upper bound, lower bound, and generalization problems

1991
We introduce E-unification, weak E-unification, E-upper bound, E-lower bound, and E-generalization problems, and the corresponding notions of unification, weak unification, upper bound, lower bound, and generalization type of an equational theory. When defining instantiation preorders on solutions of these problems, one can compared substitutions w.r.t.
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Approximating the Rainbow – Better Lower and Upper Bounds

2012
In this paper we study the minimum rainbow subgraph problem, motivated by applications in bioinformatics. The input of the problem consists of an undirected graph where each edge is coloured with one of the p possible colors. The goal is to find a subgraph of minimum order (i.e.
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Upper and Lower Bounds on Generalized Fourier Coefficients

Journal of Mathematical Physics, 1964
Methods are given for obtaining variational upper and lower bounds on the nth Fourier coefficient Cn2=|∫g*σUndτ/2 of a function g relative to a sequence of eigenfunctions Un. The methods differ in their ease of application and in the amount of information required concerning the eigenvalues associated with the Un. Some illustrative examples are given.
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Upper and lower bounds to eigenvalues

Theoretica Chimica Acta, 1969
R. P. Messmer, F. W. Birss
  +4 more sources

Recursive lower and dual upper bounds for Bermudan-style options

European Journal of Operational Research, 2020
Carlos Velasco
exaly  

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