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Topic: Chromatic index

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In the News (Wed 17 Jul 19)

  Chromatic Aberration
A lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short wavelengths) is larger than that of red light (long wavelengths).
The idea is to use a lens pair with the strongest lens of low dispersion coupled with a weaker one of high dispersion calculated to match the focal lengths for two chosen wavelengths.
Another approach to chromatic aberration reduction is to use two positive lenses separated by one half the sum of their wavelengths.
hyperphysics.phy-astr.gsu.edu /hbase/geoopt/aber2.html   (297 words)

 Page vierge 1
The oriented chromatic number ocn(G) of an oriented graph G is defined as the smallest k such that G admits an oriented k-coloring.
Moreover, we prove that the oriented chromatic number of any graph with excess k is at most k+3, except for graphs having excess 1 and containing a directed cycle on 5 vertices which have oriented chromatic number 5.
The oriented chromatic number \chi_o({G}) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relations between the oriented chromatic number and the acyclic chromatic number and some other parameters of a graph.
www.labri.fr /perso/sopena/Publis_GB.htm   (3903 words)

This photograph was taken to test the lens for chromatic aberration.
The cause of chromatic aberration is that the lens isn't able to focus all colours equally.
The center of the lens will show no chromatic aberration, while it will be worst at the periphery of the frame.
www.luminous-landscape.com /reviews/chromatic.shtml   (883 words)

 Gordon Royle's Cubic Graphs
A snark is defined to be a cyclically 4-edge connected cubic graph with chromatic index 4 and girth at least 5.
The really important part of this definition is that the graph has chromatic index 4; the statement that all cubic graphs of chromatic index 4 are non-planar is equivalent to the four-colour theorem, and hence a planar snark (a boojum) would be a counterexample to the four-colour theorem.
One of the long-standing questions was whether it was possible for the chromatic polynomial of a graph to have roots whose real parts were negative.
www.csse.uwa.edu.au /~gordon/remote/cubics   (737 words)

The required number of colors is called the chromatic index of the graph.
To do this we first formulate edge coloring as an integer program and we define the fractional chromatic index to be the optimum of its linear programming relaxation.
So it would be of interest to determine for which classes of simple graphs is the chromatic index equal to the ceiling of the fractional chromatic index as we can compute the chromatic index for graphs in these classes.
reports-archive.adm.cs.cmu.edu /anon/1998/abstracts/98-176.html   (259 words)

 JJQ Publications
Strong chromatic index of subset graphs, joint with A.T. Benjamin, Journal of Graph Theory, Vol.
Strong chromatic index in subset graphs, joint with E.L. Sundberg*, Ars Combinatoria, 49 (1998) 155-159.
Further the d-chromatic index of chordal graphs is shown to satisfy the conjectured upper bound due to Skupien for all values of d.
faculty.oxy.edu /jquinn/home/pubs.html   (1253 words)

 Graph 2005: Abstracts
The idea of a decomposition of graph occurs both in the study of intersection graphs and in combinatorial design theory.
We will show that if the host graph is a tree T, then all S -decompositions of T have the same chromatic index and this can be computed in polynomial time.
By contrast, for every tree S the problem of determining the chromatic index of an S -decomposition of a bipartite graph is NP-complete as is the problem of deciding if an integer is in the S -spectrum of a bipartite graph.
www.cri.haifa.ac.il /events/2005/graph/abstract.php?id=0025517051600t2   (301 words)

 97-59: Chromatic Index Critical Graphs of Orders 11 and 12   (Site not responding. Last check: 2007-10-14)
Chromatic Index Critical Graphs of Orders 11 and 12
We prove that there is no chromatic-index-critical graph of order 12, and that there are precisely two non-trivial chromatic index critical graphs on 11 vertices.
Together with known results this implies that there are precisely three non-trivial chromatic-index-critical graphs of order $\leq 12$.
dimacs.rutgers.edu /TechnicalReports/abstracts/1997/97-59.html   (81 words)

 97-39: Chromatic-Index Critical Graphs of Even Order   (Site not responding. Last check: 2007-10-14)
The Critical Graph Conjecture independently stated by I.T. Jakobsen (On critical graphs with chromatic index 4, Disc.
Beineke, R. Wilson (On the edge chromatic number of a graph, Disc.
Chetwynd and H. Yap (Chromatic index critical graphs of order 9, Disc.
dimacs.rutgers.edu /TechnicalReports/abstracts/1997/97-39.html   (196 words)

 BieSOn - Chromatic index critical graphs and multigraphs   (Site not responding. Last check: 2007-10-14)
BieSOn - Chromatic index critical graphs and multigraphs
We consider graphs and multigraphs which are critical with respect to the chromatic index.
In chapter 3, we give a construction of critical multigraphs with exactly 20 vertices and maximum degree k for every k>=5.
bieson.ub.uni-bielefeld.de /volltexte/2003/156   (118 words)

 chromatic number   (Site not responding. Last check: 2007-10-14)
Definition: The minimum number of colors needed to color the vertices of a graph such that no two adjacent vertices have the same color.
See also vertex coloring, chromatic index, Christofides algorithm.
Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "chromatic number", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
www.nist.gov /dads/HTML/chromatcnmbr.html   (132 words)

 [No title]
Another example is the edge chromatic number (chromatic index) of bipartite graphs which can be done in polynomial time using the maximum network flow algorithm (
to calculate the chromatic index and find an optimal edge colouring of any bipartite graph.
The circular chromatic number of a graph is the infimum of
www.cecm.sfu.ca /CAG/abstracts/GTv23coldemo.mw   (274 words)

 Atlas: On the Chromatic Spectrum of Decompositions of Graphs by Robert Jamison   (Site not responding. Last check: 2007-10-14)
Atlas: On the Chromatic Spectrum of Decompositions of Graphs by Robert Jamison
The chromatic index of a decomposition \mathscrD is the chromatic number of I(\mathscrD).
The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # casw-17.
atlas-conferences.com /cgi-bin/abstract/casw-17   (293 words)

 [No title]
Computer Bulletin September, also published by L.M.S. and I.M.A. 1988 Chetwynd, A.G. and Hilton, A.J.W. The existence of multigraphs with a given degree sequence and given chromatic index, Congressus Numerantium 58, 347-356.
1990 Chetwynd, A.G. and Hilton, A.J.W. The Chromatic index of graphs with large maximum degree, where the number of vertices of maximum degree is relatively small, Journal of Combinatorial Theory (B) 48 45-66.
On the total chromatic number of graphs of high minimum degree, Journal of London Mathematical Society (2) 44 193-202.
www.maths.lancs.ac.uk /~chetwynd/paperstog.doc   (1406 words)

 ADM Seminar   (Site not responding. Last check: 2007-10-14)
A G-decomposition of H has chromatic index chi'=k if it is k block colourable and not k-1 block colourable.
D is a G-decomposition of H} and exhibit a D that achieves this minimum.
We illustrate some design theory techniques (G-resolvable designs and G-frames and hill climbing) and use them to solve the Minimal Chromatic Index Problem, for the cases where H the complete graph on n vertices.
www.math.clemson.edu /~gmatthe/adm.html   (1919 words)

 Katsura Shareware KS Chromatic Tuner AU
Katsura Shareware KS Chromatic Tuner AU 440Forums.com
You can use KS Chromatic Tuner AU to tune your guitar, bass, and other musical instruments.
It free and fast and it'd allow you to post news, ads, messages in the forums, change your language/time setting...
www.macmusic.org /software/view.php/lang/en/id/3051   (86 words)

 Amazon.com: Erdos on Graphs : His Legacy of Unsolved Problems: Books: Fan Chung,Ronald L. Graham,Ron Graham   (Site not responding. Last check: 2007-10-14)
SIPs: infinite chromatic number, acyclic colorings, list chromatic index, hypergraph problems, made bipartite (more)
One of the main treasures Paul Erdos left us is his collection of problems, most of which are still open today.
infinite chromatic number, acyclic colorings, list chromatic index, hypergraph problems, made bipartite, chromatic graphs, extremal graph theory, critical graphs, partition relations, regularity lemma, monochromatic triangles, combinatorial number theory, infinite graphs, finite subgraphs, favorite problems, giant component, extremal problems, dense graphs, random graph, edge density, chromatic numbers, subgraph isomorphic, sparse graphs, isolated vertices, coloring problems
www.amazon.com /Erdos-Graphs-Legacy-Unsolved-Problems/dp/156881111X   (1172 words)

 MMD Archives Subject Index for: Chromatic
FS: 61-Note Chromatic Fair Organ in Toulouse, from frankoys@free.fr
Chromatic vs. Diatonic Organ Scales, from Russell Wattam
Contact our webmaster about technical problems you encounter using this web site.
mmd.foxtail.com /Archives/KWIC/C/chromatic.html   (121 words)

 Katsura Shareware Chromatic Tuner 1.4.1
It is a 12-note chromatic scale tuner application that utilizes a sound input device such as built-in microphone, line in, and iSight.
Tuning: multi-tempered chromatic scale (Equal Tempered, Kellner, Kirnberger III, Meantone, Pythagorean, Vallotti, Werckmeister III, Young II, etc.)
Fixed the crash bug with the Transpose feature on Intel Mac.
www.macmusic.org /software/version.php/lang/en/id/3709   (89 words)

 chromatic's home pages
Parsermaker — generate a standalone Perl parser module from a grammar.
Build a Quick Perl Module Database — abuse Perl the chromatic way!
Perl Monks — an off-site link where I share my dubious Perl wisdom.
www.wgz.org /chromatic   (426 words)

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