Graphs in Which any Two Colour Classes Induce a Tree (I)

Keyword(s):  
1997 ◽  
Vol 169 (1-3) ◽  
pp. 39-54 ◽  
Author(s):  
F.M. Dong ◽  
K.M. Koh
Keyword(s):  

2019 ◽  
Vol 40 (2) ◽  
pp. 149-162 ◽  
Author(s):  
Andre C. Bruinjé ◽  
Mauricio O. Moura ◽  
Bruno S. Maggi ◽  
Vinicius A. São-Pedro ◽  
Daniel M.A. Pessoa ◽  
...  

Abstract Animal colouration plays a key role in inter and intraspecific interactions, pre-eminently in mate signalling. When multiple types of colouration occur within sexes it is possible that they show alternative reproductive strategies. In lizards, most colouration studies do not incorporate how colour is perceived by conspecifics. Here, we used unbiased colour analysis methods (spectrophotometry and visual modelling) to test for sexual dimorphism and within male dichromatism in the Striped Lava Lizard. We found that males express two distinct colourations that are different from females in several dorsal and ventral body regions. Our results showed UV reflection at the throat, an important body region for signalling. Ventral patches, the coloured badge seen in adult males of Tropidurus spp., have two distinct colour classes within males (Y and B males). Morphs are best discriminated by blue and yellow chroma, and brightness. Body size had little influence on colouration, suggesting that colour may be linked to inheritance rather than growth. Our study clearly shows sexual dichromatism and the existence of colour morphs in this species. Moreover, morph differences in colouration are perceptible by conspecifics. These differences are not only between ventral patches, but also in other body parts such as the dorsum, previously considered as cryptic by human observers. We suggest that colouration at the ventral patches and throat might play a role in intraspecific interactions. Patches increase colour intensity during breeding season and are likely to be costly by pigment-based expression, whereas throat’s UV reflection might have a cost infringed by conspicuousness.


2000 ◽  
Vol 10 (2) ◽  
pp. 295-315 ◽  
Author(s):  
David Trevarthen

The cairns at Balnuaran of Clava show a structural relationship to the annual cycle, most clearly in their alignment on Midwinter sunset. The stones used in their construction fall into simple colour classes: ‘red’, ‘white’ and ‘black’. All three, but especially the black, appear to show selective arrangement in the cairns. A preliminary study of the relationships between the position of coloured stones and certain solar alignments, using both direct opposition and shadow casting, indicates that choice of colour may have been a significant factor in the positioning of stones within the monuments. Moreover the three colours seem to show a consistent pattern of meaning across a wide spectrum of cultures, which may imply a universal psychological factor in their symbolic use.


1982 ◽  
Vol 33 (3) ◽  
pp. 443 ◽  
Author(s):  
R Moss ◽  
PJ Randall ◽  
CW Wrigley

Wheat grain from sulfur-adequate plants remains straw yellow in colour when soaked in glutaraldehyde, but grain from sulfur-deficient plants turns brown or purplish brown. This observation is the basis of a proposed test to identify low-sulfur grain samples, and thus to identify sites requiring sulfur fertilizer. The colour formed during treatment with 4% glutaraldehyde in pH 6.8 phosphate buffer is ranked zero (no colour change), 1, 2 or 3 (maximum colour intensity). A glutaraldehyde score is then awarded on the basis of the percentage of grains in each of these four colour classes. Scores range from 0 to 300 with sulfur-deficient samples having scores > 100. The glutaraldehyde score was highly correlated with N/S ratio in the grain (v = 0.88***) and negatively correlated with percentage sulfur in the grain (r = -0.60** *). In a program to identify wheat-grain samples which are deficient in sulfur for breadmaking quality or yield, the glutaraldehyde test could be used in preliminary sorting to identify those samples requiring further testing.


1978 ◽  
Vol 30 (03) ◽  
pp. 455-457
Author(s):  
Barry Fawcett

This paper answers affirmatively a question of Pavol Hell [2]: if a graph admits a full n-colouring for every finite n ≧ n0, does it admit an infinité full colouring? (A colouring is full if every pair of distinct colour classes is joined by at least one edge).


1972 ◽  
Vol 15 (3) ◽  
pp. 349-354 ◽  
Author(s):  
E. J. Cockayne

By an r-graph G we mean a finite set V(G) of elements called vertices and a set E(G) of some of the r-subsets of V(G) called edges. This paper defines certain colour classes of r-graphs which connect the material of a variety of recent graph theoretic literature in that many existing results may be reformulated as structural properties of the classes for some special cases of r-graphs. It is shown that the concepts of Ramsey Numbers, chromatic number and index may be defined in terms of these classes. These concepts and some of their properties are generalized. The final subsection compares two existing bounds for the chromatic number of a graph.


2005 ◽  
pp. 40-45
Author(s):  
Zsuzsanna Tóth

The main aim of this study was to analyze sources of variability for coat colour expressed as a quantitative trait as well as to determine non genetic factors influencing horse colour variation and shades. Traditional Hungarian horse breeds such as Lipizzan (grey), Gidran (chestnut), Shagya Arabian and Arabian Pure Bred (grey) and Nonius (bay and black) horses were involved in the current study. We report results using direct measurements of horse coat colour using objective colorimetric dimensions and a spectrophotometer for determining hair melanin. Correlation analysis indicated that the single biological component that correlated best with the total melanin content of horse hair is the L* value (r=-0.858, p<0.0001). Subjective colour classes and coat colour variables L* and a* were obviously related, with R2 values of 0.88 and 0.46 respectively, with a lower R2 for b* of 0.22 (all p<0.001).


2021 ◽  
Vol 52 (4) ◽  
Author(s):  
José F. Reyes ◽  
Elías Contreras ◽  
Christian Correa ◽  
Pedro Melin

An image analysis algorithm for the classification of cherries in real time by processing their digitalized colour images was developed, and tested. A set of five digitalized images of colour pattern, corresponding to five colour classes defined for commercial cherries, was characterized. The algorithm performs the segmentation of the cheery image by rejecting the pixels of the background and keeping the image features corresponding to the coloured area of the fruit. A histogram analysis was carried out for the RGB and HSV colour spaces, where the Red and Hue components showed differences between each of the specified colour patterns of the exporting reference system. This information led to the development of a hybrid Bayesian classification algorithm based on the components R and H. Its accuracy was tested with a set of cherry samples within the colour range of interest. The algorithm was implemented by means of a real time C++ code in Microsoft Visual Studio environment. When testing, the algorithm showed a 100% effectiveness in classifying a sample set of cherries into the five standardized cherry classes. The components of the hardware-software system for implementing the methodology are low cost, thus ensuring an affordable commercial deployment.


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