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Journal articles on the topic "Dichromatic number":
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Pleanmani, Nopparat, and Sayan Panma. "Bounds for the dichromatic number of a generalized lexicographic product of digraphs." Discrete Mathematics, Algorithms and Applications 08, no. 02 (May 26, 2016): 1650034. http://dx.doi.org/10.1142/s1793830916500348.
A subset [Formula: see text] is acyclic if it induces an acyclic subdigraph of a digraph [Formula: see text] and the dichromatic number [Formula: see text] of [Formula: see text] is defined to be the minimum integer [Formula: see text] such that [Formula: see text] can be partitioned into [Formula: see text] acyclic subsets. In this paper, we obtain lower and upper bounds for the dichromatic number of a generalized lexicographic product and the dichromatic number of a generalized corona of digraphs in terms of dichromatic numbers of those digraphs.
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Gishboliner, Lior, Raphael Steiner, and Tibor Szabó. "Dichromatic number and forced subdivisions." Journal of Combinatorial Theory, Series B 153 (March 2022): 1–30. http://dx.doi.org/10.1016/j.jctb.2021.10.002.
Hochstättler, Winfried. "A flow theory for the dichromatic number." European Journal of Combinatorics 66 (December 2017): 160–67. http://dx.doi.org/10.1016/j.ejc.2017.06.020.
Ellis, Paul, and Dániel T. Soukup. "Cycle reversions and dichromatic number in tournaments." European Journal of Combinatorics 77 (March 2019): 31–48. http://dx.doi.org/10.1016/j.ejc.2018.10.008.
Joó, Attila. "Uncountable dichromatic number without short directed cycles." Journal of Graph Theory 94, no. 1 (October 21, 2019): 113–16. http://dx.doi.org/10.1002/jgt.22509.
Bataineh, Khaled. "On the skein theory of dichromatic links and invariants of finite type." Journal of Knot Theory and Its Ramifications 26, no. 13 (November 2017): 1750092. http://dx.doi.org/10.1142/s0218216517500924.
In [Dichromatic link invariants, Trans. Amer. Math. Soc. 321(1) (1990) 197–229], Hoste and Kidwell investigated the skein theory of oriented dichromatic links in [Formula: see text]. They introduced a multi-variable polynomial invariant [Formula: see text]. We use special substitutions for some of the parameters of the invariant [Formula: see text] to show how to deduce invariants of finite type from [Formula: see text] using partial derivatives. Then we consider the 2-component 1-trivial dichromatic links. We study the Vassiliev invariants of the 2-component in the complement of the 1-component, which is equivalent to studying Vassiliev invariants for knots in [Formula: see text] We give combinatorial formulas for the type-zero and type-one invariants and we connect these invariants to existing invariants such as Aicardi's invariant. This provides us with a topological meaning of the first partial derivative, which is also shown to be universal as a type-one invariant.
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LINHARES, JOÃO M. M., PAULO D. PINTO, and SÉRGIO M. C. NASCIMENTO. "The number of discernible colors perceived by dichromats in natural scenes and the effects of colored lenses." Visual Neuroscience 25, no. 3 (May 2008): 493–99. http://dx.doi.org/10.1017/s0952523808080620.
The number of discernible colors perceived by normal trichromats when viewing natural scenes can be estimated by analyzing idealized color volumes or hyperspectral data obtained from actual scenes. The purpose of the present work was to estimate the relative impairment in chromatic diversity experienced by dichromats when viewing natural scenes and to investigate the effects of colored lenses. The estimates were obtained computationally from the analysis of hyperspectral images of natural scenes and using a quantitative model of dichromats' vision. The color volume corresponding to each scene was represented in CIELAB color space and segmented into cubes of unitary side. For normal trichromats, the number of discernible colors was estimated by counting the number of non-empty cubes. For dichromats, an algorithm simulating for normal observers the appearance of the scenes for dichromats was used, and the number of discernible colors was then counted as for normal trichromats. The effects of colored lenses were estimated by prior filtering the spectral radiance from the scenes with the spectral transmittance function of the lenses. It was found that in dichromatic vision the number of discernible colors was about 7% of normal trichromatic vision. With some colored lenses considerable improvements in chromatic diversity were obtained for trichromats; for dichromats, however, only modest improvements could be obtained with efficiency levels dependent on the combination of scene, lens and type of deficiency.
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Lin, Huiqiu, and Jinlong Shu. "Spectral radius of digraphs with given dichromatic number." Linear Algebra and its Applications 434, no. 12 (June 2011): 2462–67. http://dx.doi.org/10.1016/j.laa.2010.12.026.
Hochstättler, Winfried. "Towards a flow theory for the dichromatic number." Electronic Notes in Discrete Mathematics 49 (November 2015): 101–6. http://dx.doi.org/10.1016/j.endm.2015.06.016.
STOŠIĆ, MARKO. "CATEGORIFICATION OF THE DICHROMATIC POLYNOMIAL FOR GRAPHS." Journal of Knot Theory and Its Ramifications 17, no. 01 (January 2008): 31–45. http://dx.doi.org/10.1142/s0218216508005975.
For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate n-specialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs. Also, for each graph and integer n ≤ 2, we define the different one-variable n-specializations of the dichromatic polynomial, and for each polynomial, we define graded chain complex whose graded Euler characteristic is equal to that polynomial. Furthermore, we explicitly categorify the specialization of the Tutte polynomial for graphs which corresponds to the Jones polynomial of the appropriate alternating link.
Cette thèse est dédiée à l'étude de la dicoloration, une notion de coloration pour les digraphes introduite par ErdH{o}s et Neumann-Lara à la fin des années 1970, ainsi que le paramètre qui lui est associé, à savoir le nombre dichromatique. Au cours des dernières décennies, ces deux notions ont permis de généraliser de nombreux résultats classiques de coloration de graphes.Nous commençons par donner différentes bornes sur le nombre dichromatique des digraphes dont le graphe sous-jacent est un graphe cordal. Ensuite, nous améliorons la borne donnée par le théorème de Brooks pour les digraphes sans arcs antiparallèles et introduisons une notion de dégénérescence variables pour les digraphes, ce qui nous permet de prouver une version plus générale du théorème de Brooks.Nous étudions ensuite les digraphes $k$-dicritiques, c'est-à-dire les obstructions minimales à la $(k-1)$-dicolorabilité. En particulier, nous généralisons un résultat de Gallai au cas dirigé, et nous prouvons une conjecture de Kostochka et Stiebitz dans le cas particulier $k=4$. Nous discutons également la densité maximum de tels digraphes, et prouvons qu'il n'y a qu'un nombre fini de digraphes semi-complets $3$-dicritiques. On donne par la suite certains résultats structurels sur les digraphes dicritiques de grand ordre.Enfin, nous étudions la notion de redicoloration pour les digraphes. En particulier, nous prouvons que de nombreux résultats soutenant la conjecture de Cereceda se généralisent au cas dirigé This thesis focuses on a notion of colouring of digraphs introduced by ErdH{o}s and Neumann-Lara in the late 1970s, namely the dicolouring, and its associated digraph parameter: the dichromatic number. It appears in the last decades that many classical results on proper graph colouring have directed counterparts using these notions.We first give a collection of bounds on the dichromatic number of digraphs for which the underlying graph is chordal. We then strengthen the Directed Brooks' Theorem on a large class of digraphs which contains digraphs without antiparallel arcs. We also introduce a notion of variable degeneracy for digraphs which leads to a more general version of this theorem.Next we prove a collection of results on $k$-dicritical digraphs, that is the digraphs that are minimal obstruction for the $(k-1)$-dicolourability. We first generalise a result of Gallai to the directed case and then prove a conjecture of Kostochka and Stiebitz in the particular case $k=4$. We also discuss the maximum density of such digraphs and prove that the number of $3$-dicritical semi-complete digraphs is finite. We then give a collection of results on the substructures in large dicritical digraphs.We finally study the notion of redicolouring for digraphs. In particular we prove that a large collection of evidences for Cereceda's conjecture admit a directed counterpart
Book chapters on the topic "Dichromatic number":
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Aboulker, Pierre, Frédéric Havet, Kolja Knauer, and Clément Rambaud. "On the Dichromatic Number of Surfaces." In Trends in Mathematics, 181–87. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83823-2_29.
Gynandromorphism is a rare phenomenon where an individual develops with a mosaic of both male and female traits. It is observed in various groups of organisms, including arthropods, birds, reptiles, amphibians, and mammals. Among arthropods, gynandromorphs have been frequently documented in both natural populations and laboratory settings. In insects, bilateral gynandromorphs are the most commonly observed, where the left and right halves of the body display different sexes. This phenomenon has been reported in 12 orders within the class Insecta. Within the order Lepidoptera (butterflies and moths), gynandromorphism has been documented in 18 families, with a higher number of cases observed in the families Papilionidae, Pieridae, and Saturniidae. Lepidopterans are known for their sexual dichromatism, primarily expressed through wing coloration. While gynandromorph specimens have been reported in various butterfly families such as Lycaenidae, Nymphalidae, Pieridae, Papilionidae, and Geometridae, there have also been documented cases in certain moth species, including Noctuidae species like Agrotis segetum and Agrotis ipsilon.
Conference papers on the topic "Dichromatic number":
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Escanaverino, Jose Martinez, Jose A. Llamos Soriz, Alejandra Garcia Toll, and Tania Ortiz Cardenas. "Rational Design Automation by Dichromatic Graphs." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21050.
Abstract As the complexity of mechanical design increases, due to larger size mathematical models, the need for rational design procedures also goes up. As shown elsewhere, dichromatic graphs have proven their value as tools for the algorithmic education of mechanical engineers. This paper analyzes the worth of such graphs as a means to achieve rational design solutions in complex industrial problems. The paper covers plant maintenance and research & development professional case studies. A real-life problem in electromechanical system reengineering is the first application example. Attention is also given in the paper on the partitioning of large problems, involving many variables and relations. The design of a planetary gear unit, with a three-digit number of elements in the mathematical model, is an example problem in this area. In addition, changes and extensions to the computational problem solving theory are included.
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Pokorny, Joel, and Vivianne C. Smith. "Color matching as a clinical tool." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.tuo2.
Color matching is the definitive technique for documenting normal color vision and for diagnosing congenital color vision defects. The efficacy of the technique lies in the widely accepted supposition that color matching directly reflects the number and spectral sensitivities of the active receptor types. Color matching behavior may be modified by systemic or ophthalmic disease. There are two major ways in which disease alters color matching; the match-midpoint may be shifted (an alteration of normal color vision) and/or the match-width may be enlarged (a reduction of normal color vision). The nature of the change often allows precise interpretation of the etiology of the functional change. Simplified procedures which we use for clinical evaluation include a match of a yellow to a mixture of red and green (the Rayleigh equation) and a match of blue-green to a mixture of blue and green (the Moreland equation). To evaluate reduced forms of color vision we use a match of a green to a mixture of red and blue (a dichromatic coefficient). Examples are given of alteration systems (both prereceptoral and retinal) and reduction systems (both receptoral and neural).
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Dunn, S., M. G. Moharam, L. Glebov, and K. R. Richardson. "Diffraction characteristics of thick phase volume hologram recorded in photo-thermo-refractive glasses." In Diffractive Optics and Micro-Optics. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/domo.1998.dthc.3.
Volume holographic optical elements have numerous applications in beam shaping, spectral filters, optical display systems, optical interconnects, and data storage. One of the primary challenges facing the development of applications involving volume holographic optics is the recording media. It must meet a number of requirements including phase volume recording with high efficiency, low scattering, large dynamic range, and high resolution, while exhibiting good thermal, chemical, and mechanical durability, as well as environmental stability. Current recording media include photographic films, dichromated gelatin, photoresists, photopolymers, photochromies, photo-organics, and photoreffactive media. These media meet only a few of the desired requirements.
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Mantravadi, Murty V. "Nondestructive thickness measurement of DCG films." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.fd3.
Dichromated gelatin (DCG) films are coated on substrates to make holographic optical elements (HOEs) by using various techniques. It is necessary to measure the thickness of these films before and after exposure and processing. It is also necessary to estimate the variation of the thickness at different areas of the substrate. This thickness range is usually between 5 03μm and 50 μm. The principle of the method is based on the measurements on the Haidinger fringes generated by the film. For ease of observation and measurement, a commercial Fizeau type interferometer such as ZYGO has been used. The simple modification to observe the Haidinger fringes with the Fizeau type interferometer will be described. The thickness of the film is related to the diameters of the Haidinger fringes. It is possible to estimate the thickness quickly by counting the number of fringes. A more accurate estimate can be obtained by the measurement of the diameters of the fringes and by using this data in a formula that will be described. It is possible to estimate the thickness of the film to within +1 μm. The method is entirely nondestructive.
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Chen, Ray T., William Phillips, Thomasz Jannson, and David Pelka. "Integration of Polymer Waveguides with HOE On GaAs, LiNbO3, Glass And Aluminum Substrates to Provide massive Fan Out (104/node) Optical Interconnects for Computing." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/optcomp.1989.pd1.
In this paper, we report good quality waveguides (loss<ldb/cm) formed from pure gelatin, i.e., gelatin without ammonium dichromate. Pure gelatin solutions with various water to gelatin ratios were spun on top of soda-lime glass (N=1.512 at 632.8nm). When gelatin first goes into aqueous solution the molecules exist as single chains encircled by water molecules. Upon standing at temperatures below 30 °C, solutions containing more than 1% gelatin become rigid through cross linking and exhibit rubber-like mechanical properties. In this work optical waveguides were thus formed. The waveguiding properties were examined through the prism coupling method. The measured effective indices for TE and TM guided waves were the same for each sample. This implies that no birefringence exists in the gelatin layer. The guiding layer index profiles of multi-mode gelatin waveguides were determined by the inverse WKB method commonly used in integrated optics[l]. Graded index profile of a multi-mode waveguide can be accurately determined by IWKB method. Step indices can also be determined through this method with a small deviation at the turning point [2]. The calculated index profile of sample #D1, composed of 15 grams of gelatin, 100 CC water and spun at 100 rpm, is given in Fig.1, curve A. The measured surface index of various samples with different water-gelatin ratios is shown in Fig.2. Surface index variation from 1.522 to 1.543 was observed. Each data point of Fig.2 was determined by the 0th order mode of the corresponding multimode waveguide (total number of modes >10). Since the guiding layer has a step index, the 0th order mode effective index is almost equal to the surface index. The plotted index profiles of the various gelatin waveguides before wet processing demonstrates that the gelatin layer forms a step index layer and the index refraction increases as the gelatin ratio increases.
