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0032 | Beyond Neutrosophic Graphs (E-Publisher) [article]

Henry Garrett
2022 Zenodo  
Some classes of neutrosophic graphs are studied in the the terms of different types of chromatic numbers and neutrosophic chromatic numbers.  ...  The tools to define specific edges are studied. One notion is to use the connectedness to have two different types of numbers which are neutrosophic chromatic number and chromatic number.  ...  Neutrosophic Chromatic Number Numbers and Sets Based on some ideas, numbers and sets are defined in the ways that, some results are obtained.  ... 
doi:10.5281/zenodo.6320305 fatcat:tduto2i2qvcvfhppczo2b3gvy4

The History of the Total Chromatic Number Conjecture [article]

Hossein Shahmohamad
2011 arXiv   pre-print
The total chromatic number conjecture which has appeared in a few hundred articles and in numerous books thus far is now one of the classic mathematical unsolved problems.  ...  Behzad is the sole author of the Total Chromatic Number Conjecture. - The wrong referrals provided by numerous authors over the last forty four years, to indicate Vizing's authorship, must be brought to  ...  Introduction The Total Chromatic Number Conjecture is stated as follows: Color all the vertexes and all the edges of a given graph G simultaneously in such a way that no two adjacent vertexes have the  ... 
arXiv:1104.3170v1 fatcat:hjv6ujyncbaynckaywkrdpb2dq

THE PROPORTIONAL COLORING PROBLEM: OPTIMIZING BUFFERS IN RADIO MESH NETWORKS

FLORIAN HUC, CLÁUDIA LINHARES SALES, HERVÉ RIVANO
2012 Discrete Mathematics, Algorithms and Applications (DMAA)  
We finally identify a class of graphs and a class of weighted graphs for which the proportional chromatic index can be exactly determined.  ...  It consists in finding a minimum cost edge coloring of a graph which preserves the proportion given by the weights associated to each of its edges.  ...  In consequence, a set of simultaneously achievable calls induces a matching on the graph.  ... 
doi:10.1142/s1793830912500280 fatcat:emio65lztvhaxduouksoqv6cfe

The Proportional Colouring Problem: Optimizing Buffers in Wireless Mesh Networks

Florian Huc, Cláudia Linhares-Sales, Hervé Rivano
2008 Electronic Notes in Discrete Mathematics  
We finally characterize some graphs and weighted graphs for which we can determine the proportional edge chromatic number.  ...  If such colouring exists, we want to find one using the minimum number of colours.  ...  If such colouring exists, we want to find one using the minimum number of colours, number which we call proportional edge chromatic number.  ... 
doi:10.1016/j.endm.2008.01.025 fatcat:qnoawmjwyfgtlkamokbdvtjoxu

Strong Fuzzy Chromatic Polynomial (SFCP) of Fuzzy Graphs and Some Fuzzy Graph Structures with Applications

Mamo Abebe Ashebo, Venkata Naga Srinivasa Rao Repalle
2020 Pure and Applied Mathematics Journal  
In this work, we introduce the new concept, called strong fuzzy chromatic polynomial (SFCP) of a fuzzy graph based on strong coloring.  ...  The SFCP of a fuzzy graph counts the number of k-strong colorings of a fuzzy graph with k colors.  ...  Besides counting the strong colorings on fuzzy graphs, SFCP can be used to get the strong fuzzy chromatic number of a fuzzy graph.  ... 
doi:10.11648/j.pamj.20200901.13 fatcat:mb2q7iu3cvg3pcrxheh4oozbwm

Page 2566 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
The authors complement previous work on the chromatic number of diagrams of posets [J. NeSetril and V.  ...  Summary: “In this paper, the bounds for the 4-chromatic numbers nN me--* bn oD we oOo  ... 

A note on total colourings of digraphs

Małgorzata Zwonek
2006 Discrete Mathematics  
In one of these colourings we show that the problem of calculating the total chromatic index reduces to that of calculating the chromatic number of the underlying graph.  ...  In the other colouring we find the total chromatic indices of complete symmetric digraphs and tournaments.  ...  Let us start with some additional remarks concerning the estimate of the total chromatic index of the second type. Note that (G(D)) = (D).  ... 
doi:10.1016/j.disc.2006.04.016 fatcat:utfbeddsnzh67c2wquew6nqy4e

Page 1294 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
Some of these are planarity, number of arcs or edges, length of a longest directed path, chromatic number, domination number and node independence number.  ...  However, both constructions are based on inductive arguments, solving the problem for graphs and hypergraphs simultaneously.  ... 

Page 43 of Biological Reviews Vol. 76, Issue 4 [page]

2001 Biological Reviews  
Cephalopod chromatophores locomotor 1989). components (Hanlon & Wolterding, ‘These numbers give some idea of the numbers of chromatic components available to some common inshore cephalopods, and also the  ...  characteristics. differences in chromatic behaviour.  ... 

A lower bound on the chromatic number of Mycielski graphs

Massimiliano Caramia, Paolo Dell'Olmo
2001 Discrete Mathematics  
In this work we give a new lower bound on the chromatic number of a Mycielski graph Mi. The result exploits a mapping between the coloring problem and a multiprocessor task scheduling problem.  ...  The tightness of the bound is proved for i = 1; : : : ; 8.  ...  The some reasons apply to the slight improvement on !  ... 
doi:10.1016/s0012-365x(00)00261-2 fatcat:6226h6l63vgixcv72ofdnoqe2i

On the Somatic Chromosomes in Lathyrus

Basudev Roy
1936 CYTOLOGIA  
It is interesting to note here that two processes go on simultaneously namely the corroding of the nucleolus and the increase in chromatici ty of the chromosomes.  ...  It is very important to record that some of the prophase chromo somes showed beaded appearance of their chromonemata, though these beads were few in number.  ... 
doi:10.1508/cytologia.7.424 fatcat:dzhz7i5egvel5pi7lrkqbiiamm

Implementations of a novel algorithm for colour constancy

F. Martínez-Verdú, M.J. Luque, J. Malo, A. Felipe, J.M. Artigas
1997 Vision Research  
In agreement with the principles of the relativistic model proposed by Creutzfeldt et aL, with the photometric rule (lightness anchoring rule) and with the influence of simultaneous contrast in the appearance  ...  The statistical stability of the descriptors for Munsell samples under different illuminants is good.  ...  The perceptual phenomenon of simultaneous contrast or chromatic induction, on the other hand, gives evidence of one mechanism by which the visual system may compute constant chromatic attributes in continually  ... 
doi:10.1016/s0042-6989(96)00327-6 pmid:9274768 fatcat:wwfqz26cibdwvjymaefwdkznse

Local chromatic number and distinguishing the strength of topological obstructions

Gábor Simonyi, Gábor Tardos, Siniša T. Vrećica
2008 Transactions of the American Mathematical Society  
We show that two specific topological obstructions that have the same implications for the chromatic number have different implications for the local chromatic number.  ...  The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G.  ...  Csorba, Gábor Elek, László Fehér, László Lovász, Jiří Matoušek, Gábor Moussong, András Szűcs, and RadeŽivaljević for many clarifying conversations and e-mail messages that improved our understanding of the  ... 
doi:10.1090/s0002-9947-08-04643-6 fatcat:q5o4xcyod5gghaxhaxsr6edbd4

Page 5476 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
2002h:05066 05 spot but never published, and some additional remarks.  ...  Thus we can classify graphs into two types depending on the value of their edge covering chromatic numbers.  ... 

Local chromatic number and distinguishing the strength of topological obstructions [article]

Gábor Simonyi, Gábor Tardos, Siniša T. Vrećica
2007 arXiv   pre-print
We show that two specific topological obstructions that have the same implications for the chromatic number have different implications for the local chromatic number.  ...  The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G.  ...  Csorba, Gábor Elek, László Fehér, László Lovász, Jiří Matoušek, Gábor Moussong, András Szűcs, and RadeŽivaljević for many clarifying conversations and e-mail messages that improved our understanding of the  ... 
arXiv:math/0502452v2 fatcat:s3flbdwiefeltnhrmmj43immey
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