scholarly journals K_3-WORM colorings of graphs: Lower chromatic number and gaps in the chromatic spectrum

2016 ◽  
Vol 36 (3) ◽  
pp. 759 ◽  
Author(s):  
Csilla Bujtás ◽  
Zsolt Tuza
Keyword(s):  
Chromatic Number ◽  
Chromatic Spectrum

scholarly journals On the Upper and Lower Chromatic Numbers of BSQSs(16)

10.37236/1550 ◽  
2000 ◽  
Vol 8 (1) ◽  
Author(s):  
Giovanni Lo Faro ◽  
Lorenzo Milazzo ◽  
Antoinette Tripodi
Keyword(s):  
Chromatic Number ◽  
Chromatic Numbers ◽  
New Information ◽  
Chromatic Spectrum ◽  
Minimum Numbers ◽  
Mixed Hypergraph

A mixed hypergraph is characterized by the fact that it possesses ${\cal C}$-edges as well as ${\cal D}$-edges. In a colouring of a mixed hypergraph, every ${\cal C}$-edge has at least two vertices of the same colour and every ${\cal D}$-edge has at least two vertices coloured differently. The upper and lower chromatic numbers $\bar{\chi}$, $\chi$ are the maximum and minimum numbers of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph, upper and lower chromatic numbers are applied to $SQSs$. In fact a BSQS is an SQS where all the blocks are at the same time ${\cal C}$-edges and ${\cal D}$-edges. In this paper we prove that any $BSQS(16)$ is colourable with the upper chromatic number $\bar{\chi}=3$ and we give new information about the chromatic spectrum of BSQSs($16$).

Packing Chromatic Number of Cycle Related Graphs

2014 ◽  
Vol 4 (1) ◽  
pp. 27
Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

scholarly journals On metric chromatic number of comb product of ladder graph

2021 ◽  
Vol 1836 (1) ◽  
pp. 012026
Author(s):  
M Y Rohmatulloh ◽  
Slamin ◽  
A I Kristiana ◽  
Dafik ◽  
R Alfarisi
Keyword(s):  
Chromatic Number ◽  
Ladder Graph

scholarly journals Integumentary Colour Allocation in the Stork Family (Ciconiidae) Reveals Short-Range Visual Cues for Species Recognition

Birds ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 138-146
Author(s):  
Eduardo J. Rodríguez-Rodríguez ◽  
Juan J. Negro
Keyword(s):  
Short Range ◽  
Visual Cues ◽  
Species Recognition ◽  
The Body ◽  
Whole Body ◽  
Divergent Evolution ◽  
Black And White ◽  
Extant Species ◽  
Chromatic Spectrum ◽  
Mixed Species Flocks

The family Ciconiidae comprises 19 extant species which are highly social when nesting and foraging. All species share similar morphotypes, with long necks, a bill, and legs, and are mostly coloured in the achromatic spectrum (white, black, black, and white, or shades of grey). Storks may have, however, brightly coloured integumentary areas in, for instance, the bill, legs, or the eyes. These chromatic patches are small in surface compared with the whole body. We have analyzed the conservatism degree of colouration in 10 body areas along an all-species stork phylogeny derived from BirdTRee using Geiger models. We obtained low conservatism in frontal areas (head and neck), contrasting with a high conservatism in the rest of the body. The frontal areas tend to concentrate the chromatic spectrum whereas the rear areas, much larger in surface, are basically achromatic. These results lead us to suggest that the divergent evolution of the colouration of frontal areas is related to species recognition through visual cue assessment in the short-range, when storks form mixed-species flocks in foraging or resting areas.

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