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Suryaprakash N Rao

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ODE TO HOLI – FESTIVAL OF COLORS – 2011
By Suryaprakash N Rao   
Rated "G" by the Author.
Last edited: Sunday, July 29, 2012
Posted: Saturday, August 06, 2011

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Colors are integral part of Universe. It is hard to imagine Universe devoid of colors.

 

TRADITION
View Full Article using Link:
 

 

ODE TO HOLI
– FESTIVAL OF COLORS – 2011
 
 
Petersen graph
 
 
  
Hindu Art Sand in Color
 
 
Annual celebration Holi truly Hindu on day full moon
Rightly christened a Festival of colors with colors in colors
Express joy marking end of harsh winter a reason soon
Community join live act of playing with hues valors
 
Age old ancient Hindu traditions spawn
Begin routine sweep and clean day’s dawn
Level ground with dung mixed waters cozy
Complex drawings entrance choice in dozens hazy
Every house front door decorated in reception
With Rangoli a color sand art rich in collection
 
Colors exist and existed since creation
Color means singular to life forms diverse consult
Touch feelers primitive a guide in simulation
Serves purpose saves from savage assault
 


 
Universe colorful captured in spectrum bright
Color blind nonetheless in Black & White sight
Gray tone- a parameter in extra makes plenty
Enabling shades several to distinguish bounty
 
Seeing sensors beginning unknown origins carnival
Deprived life forms thrived in competition tight
Vision under evolution instinct sustain survival
Sight during day demand even through dusk to night
Eyes in design studded with multitude lenses in special
Enhance beam meager from starry night sky sheen crucial
 
On hang around stealthy Eurasian eagle owl
Cats in variety evolved apt to ambience fit for survival
Pallas, Black-footed, fishing cats, sandcat, bearcat and Caracal
Fennec fox, clouded-leopard, aardvark, ocelot, vampire bat in parallel
 
Color vision weak in variety wilder beast or zebra in migration
Misses detection of lion or leopard presence in camflouge aberration
Unaware an easy target prey, a predator on prowl aggravation
Hierarchy well set in evolution a result significant combination
 
Human made device camera for capture
Thermal one twilight vision in rupture
Infra red enabling sight at dusk or night image
Fit for purpose fix on tree or stick on skin enabling gauge
Record animal life or activity in flight shy or stealthy
All through day or night in jungle, rural or suburb wealthy
 


 
Meaning of Color at variance in context singular
Man’s choice wavelength on weight brighter regular
Red shade in signal warns and stops strict diet
Green sign signals clear path move in quiet
Orange tinge signs system share in transit
Parties pursue rules of protection for right exit
Implied none above or below, last or first
Follow secure path safety for all count test


 
   
Francis Guthrie (1831-1899)
Guthrie’s dilemma
 
Daily routine a Combinatorist profession in no exception
Plays with a dye on diagram, map or graph at reception
Guide to chemical waste combination - safety from blast
Be it a network in service or a timetable schedule cast
 
In coloring a graph assign a dye to every node
No two neighbouring in colours same convince code
Number in painting with colours least launch chromatic
Three hues in ample for simpler or most maps mundane dramatic
An additional fourth in demand for some exceptional
A region bordered by an odd number present conditional
 
As said in Theory of Graphs a true translation
Four-colors in plenty painting a map on a plane partition
Regions sharing boundary in common accept colors unlike
Guthrie's problem emerges first to conjecture in 1852 on bike
Augustus de Morgan an honest vital instrument to popularise
Cayley in 1878 accredited first document in publication vitalise
False proofs and fake examples instances many gave rise
"Every planar graph is four-colorable" prove or disprove voice in raise


 
 
Alfred Kempe (1849-1922)
 
Regions and Chains
 
 
Coloring trait tops test in trade traditional
Passed on from generation to generation occupational
But realization recognition and demonstration
Coloring map regions just with four shades in production
Not an easy task an ordeal over time hope fades
AKempe in 1879 first to presenting a proof in public
Came to be known ‘method of Kempe chains’ symbolic
 
Percy John Heawood (1861-1955)
 
 
The Heawood graph:
chromatic number 2. crossing number 3. chromatic index 3
 
Kempe's proof in agreement lives on for a year and a decade
An announcement in 1890 from PJHeawood not for good made
News rather destructive than constructive instead
A defect in detect in testimony recognised stood
A map with 18 or 9 faces in evidence survived
An alternate declaration for sure five colors suffice to credit
Marks a beginning of Color romance pairs coming close to split
 
 


 
Peter Guthrie Tait (1831-1901)
No two edges coming from
The same vertex share the same color
 
PGTait in 1880 inspired makes in faith second attempt
With bright ideas but again a proof in error prone built
Petersen in 1891 again after a year and a decade later
Detected a gap in Tait’s proof endorsed to alter
 
  
                                                             Julius Peterson (1839-1910)        WTTutte (1917-2002)
Tutte’s graph and spiral three edge coloring
 
Tait found formulation the 4CT equivalence bearing
Every cubic plane graph with no cut-edge has an edge 3-coloring
Tait in 1884 amongst related works proposed the speculation
Every 3-connectedplanarcubic graph is Hamiltonian
WTTutte (1946) disproved with a counterexample
A graph with 25 faces, 69 edges and 46 vertices only a sample
Using three copies of Walther graph now known WTTutte’s graph best
Barnette-Bosák-Lederberg in 1965 found graph of order 38 the smallest
 
Barnette-Bosák-Lederberg Graph
 
Ferro debunked for alleged short proofs contempt
Opens up unsettled 4-CC fresh again for bright cult
A challenge to GT World to all Mathematicians in bait
Physicists pride plan plunge in pond public provoke
Identified and branded a notorious graph theory disease invoke
Scientific American, April, 1975 Martin Gardner
 
April Fool's cruel joke by Martin Gardner shook GT grounds
A map manufactured with regions 110 claiming five colors a must
Tight sittings hours passed by result in no answer sounds
SWagon 1998 in offer a four coloring hit using Mathematica trust
Colours six suffice for zero genus an improvement to five viable
But trim this number all the way to four proved knotty gamble
If the 4-CC were false a map requiring five colors constructible
Crux of proof makes obvious nonexistence a counterexample minimal
Kenneth Appel and Wolfgang Haken
 
In 1976 KAppel & WHaken hoist a proof settling 4-CC at last
Assistance algorithmic from JAKochcomputer-assisted proof cast
An exhaustive analysis scores of discrete cases to verify with caution
The first major theorem using computers in celebrations
Infinitude of possible maps reducible to 1936 configurations
Further shortened to 1476 to be checked all by supercomputers
Each not part of a smallest counterexample generations
Any map must have a portion that looks like one of these matters
Verification involving pages of laborious hand calculations
 


 
Errera’s incomplete four coloring
 
No smallest counterexamples existed or in construct
Any must contain, yet not contain, one of these might obstruct
A contradiction meaning no counterexamples exist right
Demonstrating the 4-CC truth without doubt insight
Consumed over a thousand CPU hours indebt
Celebration achievement by University of Illinois
Release of postmark Four Colours Suffice!
Mark and mind for grand success entice
 
Heinrich Heesch (1906-1995)
Main ingredients: reducibility and discharging
 
Part proof computer verified gained wider acceptance and doubts
A simpler proof similar ideas and still relying on computers
Algorithm quadratic configurations 633 reduced set unavoidable
In 1997 by Robertson, Sanders, Seymour, and Thomas
Yet another proof in 2005 by Georges Gonthier pops
Use of general purpose theorem proving software hops
Independent proof by Robertson et al. to signify
A formulation in the equational logic program Coq
Confirming validity clarity in steps clear folly fog


 
The Birkhoff’s diamond
A maximal dichromatic coloring
 
Rumours in 1980s a flaw in the Appel-Haken proof
Ulrich Schmidt at RWTH Aachen examined safe roof
Obliged in a detailed article- magnum opus in print
A book in 1989 claiming complete and detailed evidence
Attempts continue for alternate proofs worldwide confidence
 
Heawood map and double-spiral coloring
 
Spiral or double spiral chain ICahit’s Victorian approach
Birkoff’s diamond an inspirational starting point encroach
Isolate bad example graphs for Kempe’s argument for insight fill gaps
Maximal mono- and di-chromatic colourings of high and low land maps
Twin graphs in make for troubles in inner and outer faces convenience
Enhanced visual abstraction and non-computer proof a consequence
  
Fritsch, Soifer, Errera
 
  
Poussin, Kittell, Heawood
 
Known counterexamples to Kempe’s proof
 With double-spiral chain decompositions
 


 
Thomas L. Saaty
Presented 29 equivalent formulations of the 4CT
 
Proof by ADharwadker yet another new approach
Topological and Algebraic in qualification coach
Using Steiner systems and Tit’s inequality threshold four
Eilenberg modules Hall matchings and Riemann surfaces
 
Color romance continues across minds in capture world over
Nature on nerves reveals facts in earthly processes turn over
More in treasure unknown manifest secrets hidden unveil
Survival top priority taste in test world extraterrestrial
 
         
Percy Heawood (1861-1955)
                                                                       Klein bottle                  Heawood Four-Color Graph
 
SURYAPRAKASH RAO
 


 
  
William Rowan Hamilton (1805-1865)
                                                                         Dodecahedron        Icosahedron-golden-rectangles
 
Related Web Links
 
DUE RESPECTS & ACKNOWLEDGEMENTS
Attempts many approaches different
From corners of the vast world concurrent
A few in mention
SWHamilton, ACayley, LCarroll, PMayer,
Howard Levi for Algebraic Approach dear
List incomplete and unending utterance
To all those contributors not in reference
 
MISSION ACCOMPLISHED
Time hath tied terse reasons various unknown
Focus on connoisseur Combinatorists well known
Remember recall esteem extraordinary activities in lead
Salutes to great souls share deeds noble abide guide plead
Graph Theory and Block Designs in fusion repercussion
Constructs and clarifications from one for problems in other discussion
Solutions sought easily otherwise intricate burdensome
GT evolving encompassing with fast dispersal in domains alien
Be it worldwide web, Networks of Electronics or Transportation
An attest a Universal language in the background an assertion
Theories of Sciences Physical, Chemical or Social bearing
Applications in Computer, Civil, Mechanical Engineering
Name one or any GT term certain has its footprint uncanny
An easy tool GT a mirror a glance at one’s own image shiny
 

 


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Reviewed by Ibrahim Cahit (Reader) 9/30/2011
Spiral or double spiral chain ITait’s Victorian approach



should read as



Spiral or double spiral chain ICahit’s Victorian approach

Link

http://www.flickr.com/photos/49058045.N00/

for the graphical pictures should be also given.



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