1,750,939 research outputs found
The fractional chromatic number of triangle-free subcubic graphs
No full textHeckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14 / 5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32 / 11 ≈ 2.909
Chromatic roots are dense in the whole complex plane
No full textI show that the zeros of the chromatic polynomials P-G(q) for the generalized theta graphs Theta((s.p)) are taken together, dense in the whole complex plane with the possible exception of the disc \q - l\ < l. The same holds for their dichromatic polynomials (alias Tutte polynomials, alias Potts-model partition functions) Z(G)(q,upsilon) outside the disc \q + upsilon\ < \upsilon\. An immediate corollary is that the chromatic roots of not-necessarily-planar graphs are dense in the whole complex plane. The main technical tool in the proof of these results is the Beraha-Kahane-Weiss theorem oil the limit sets of zeros for certain sequences of analytic functions, for which I give a new and simpler proof
Algebraic Properties of Chromatic Polynomials and Their Roots
No full textIn this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple families of graphs. We then compute the Galois groups of chromatic polynomials of some sub-families of an infinite family of graphs (denoted {Gp,q }) and prove a conjecture posed in [15] concerning the Galois groups of one specific sub-family. Finally we investigate a conjecture due to Peter Cameron [8] that says that for any algebraic integer α there is some n ∈ ℕ such that α + n is the root of some chromatic polynomial. We prove the conjecture for quadratic and cubic integers and provide strong computational evidence that it is true for quartic
and quintic integers
The harmonious chromatic number of almost all trees
No full textA harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer m, let Q(m) be the least positive integer k such that (*) S: m. We show that for almost all unlabelled, unrooted trees T, h(T) = Q(m), where m is the number of edges of T.Copyright © Cambridge University Press 199
High-speed chromatic dispersion monitoring of a two-channel WDM system using a single TPA microcavity
No full textChromatic dispersion monitoring of two 160 Gb/s wavelength channels using a TPA Microcavity is presented. As the microcavity exhibits a wavelength resonance characteristic, a single device could monitor a number of different WDM-channels sequentially
Bounds on the complex zeros of (Di)Chromatic polynomials and Potts-model partition functions
No full textWe show that there exist universal constants C(r) such that, for all loopless graphs G of maximum degree less than or equal to r, the zeros (real or complex) of the chromatic polynomial P-G(q) lie in the disc \q\ 7.963907r. This result is a corollary of a more general result on the zeros of the Potts-model partition function Z(G)(q. {v(e)}) in the complex antiferromagnetic regime \1 + v(e)\ less than or equal to 1. The proof is based on a transformation of the Whitney-Tutte-Fortuin-Kasteleyn representation of Z(G)(q,:{v(e)}) to a polymer gas. followed by verification of the Dobrushin-Kotecky-Preiss condition for nonvanishing of a polymer-model partition function. We also show that, for all loopless graphs G of second-largest degree less than or equal to r, the zeros of P-G(q) lie in the disc \q\ < C(r)+ 1. Along the way, I give a simple proof of a generalized (multivariate) Brown-Colbourn conjecture on the zeros of the reliability polynomial for the special case of series-parallel graphs
Analysis of Chromatic Aberration Effects in Triple-Junction Solar Cells Using Advanced Distributed Models
No full textThe consideration of real operating conditions for the design and optimization of a multijunction solar cell receiver-concentrator assembly is indispensable. Such a requirement involves the need for suitable modeling and simulation tools in order to complement the experimental work and circumvent its well-known burdens and restrictions. Three-dimensional distributed models have been demonstrated in the past to be a powerful choice for the analysis of distributed phenomena in single- and dual-junction solar cells, as well as for the design of strategies to minimize the solar cell losses when operating under high concentrations. In this paper, we present the application of these models for the analysis of triple-junction solar cells under real operating conditions. The impact of different chromatic aberration profiles on the short-circuit current of triple-junction solar cells is analyzed in detail using the developed distributed model. Current spreading conditions the impact of a given chromatic aberration profile on the solar cell I-V curve. The focus is put on determining the role of current spreading in the connection between photocurrent profile, subcell voltage and current, and semiconductor layers sheet resistance
Franck-Delaplace/Chromatic-Community-Structure: Version 1.19
No full textChromatic Community Structure Analysis (ChroCoS
Franck-Delaplace/Chromatic-Community-Structure: VERSION 1.13
No full textChromatic Community Structure Analysis (ChroCoS
Franck-Delaplace/Chromatic-Community-Structure: Version 1.15
No full textChromatic Community Structure Analysis (ChroCoS
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