So it suffices to prove the four color theorem for triangulated graphs to prove it for all planar graphs, and without loss of generality we assume the graph is triangulated.

However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality ; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. ( In other words, it is a collection of sets of size k .) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on.

So the Desargues graph is one of only seven symmetric Generalized Petersen graphs.

So some database management systems use an alternative rule-based approach that uses a query graph model.

Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.

So successful has been this program, worked out by white and Negro civic leaders, that further extensions are expected in the next few months.

So with four complete Push-Pull Super-Sets No. 1, four of No. 2, four of No. 3 and four to six sets of the Incline Bench Press, you can see that Henri De Courcy has had a terrific mass-building, muscle-shaping, torso-defining workout that cannot be improved upon.

So, in the last couple of years, abstract expressionism has tended toward romantic suggestion -- indications of landscape or living figures.

So far in history man has been too greatly over-occupied with projecting things into his environment rather than first creating the sort of person who can make the highest use of the things he has created.

So this proxy situation has set up at least a partial barrier between the medium's ESP and the absent sitter's mind.

So, after the sitting has been held, several readings at one time are mailed, and the distant sitter ( whose name or whose communicator's name was given to the medium ) must mark each little item as Correct ( Hit ), Incorrect ( Miss ), Doubtful, or Especially Significant ( applying to him and, he feels, not to anyone else ).

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

So obvious are these advantages that nearly 95 per cent of the population of New York State now has access to a system, and enthusiastic librarians foresee the day, not too distant, when all the libraries in the state will belong to a co-op.

Equally penetrating in its fashion is the following remark by a lady in the course of a literary conversation: `` So much has already been written about everything that you can't find out anything about it ''.

So far as I know, the Comedie has never put Moliere's people in the costumes of the 20th century, but they do reinterpret plays and characters.

So much untidiness of mind and household does not attract the interest of the theatergoer ( unless he has been living in a gilded palace, perhaps, and wants a real big heap of contrast ).

So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming.

So Armenia has to maintain good relations at least with Iran and Georgia though international pressure against trade with Iran and while separatist tends of Armenian minority in Javakheti.

So, if a person has lived a good life, they will be rewarded in the afterlife.

So one has to introduce the charge conjugate antiparticle field, with its own creation and annihilation operators satisfying the relations

( So prevalent are these isolated peaks and ridges that a specialised term has been adopted in Germany to describe this kind of country, thought to be in great part the result of wind action.

She has referenced this independence from major labels in song more than once, including " The Million You Never Made " ( Not A Pretty Girl ), which discusses the act of turning down a lucrative contract, " The Next Big Thing " ( Not So Soft ), which describes an imagined meeting with a label head-hunter who evaluates the singer based on her looks, and " Napoleon " ( Dilate ), which sympathizes sarcastically with an unnamed friend who did sign with a label.

So broad a notion has inevitably been elusive and controversial in the history of philosophy, beginning in western philosophy with attempts among the pre-Socratics to deploy it intelligibly.

" So here is the balance NBC has to consider: The Who, ' Animal Practice.

" So, to be born again means to be saved because in order to be saved one has to confess Jesus is Lord with one's mouth and believe it in one's heart.

So, some say, we can say that that relation has being.

So far, only a single bird species, which has not been named, has been confidently identified from both above and below the K-Pg boundary ( it is present in the Maastrichtian Hell Creek Formation and Danian Fort Union Formation ).

So an eclipse cycle is any period P for which approximately holds:

So we can make do with a short table of 14 values, one for every new or full moon in a full moon cycle.

So we should correct the basic cycle ( of 1 full moon cycle ~ 14 lunations ) after 18 full moon cycles ; with the proper epoch ( starting date ), this can be done by skipping the first entry of the first full moon cycle ( of the next large cycle of 18 full moon cycle ), i. e. use the entry with value-8 instead of 0 from the first basic 14-month table above.

So this approach is not amenable to further analysis of the cycle.

So after 19 years the epact must be corrected by + 1 in order for the cycle to repeat over 19 years.

So the second cycle will go further than the first, and the process will continue, each successive phase building on and improving on what went before.

So the quantum condition integral is the average value over one cycle of the

So far there is no generally accepted theoretical explanation for them, even though a close relation to the solar cycle is evident, as they have a period of eleven years, as was known since they were first observed in 1980.

* The Prius's Not So Secret Gas-Mileage Secrets-how the Prius uses the Atkinson cycle to get better results than an Otto cycle engine

So, a combined cycle plant has a thermodynamic cycle that operates between the gas-turbine's high firing temperature and the waste heat temperature from the condensers of the steam cycle.

So, when the route upstream became blocked, the cycle was broken.

So embroiled did these two races become, so involved in their own conflict over their philosophies that they themselves lost their way, setting up an endless cycle of wars in which the younger races were pitted against each other as pawns.

So, in order to please the dogs they are going to meet at Heaven's doors after death, so they would be allowed in Heaven, people mark the 14th day of the lunar cycle in November as Kukur-tihar, as known in Nepali language for the dog's day.

So, Hirsch proved that competitive Lotka – Volterra systems cannot exhibit a limit cycle for N < 3, or any torus or chaos for N < 4.

So, it is a cycle of internalization and externalization of consciousness itself, relating to the most elevated plane in creation ( Śiva-Śakti Tattva ).

So high-temperature MHD was developed as a topping cycle to increase the efficiency of electric generation, especially when burning coal or natural gas.

So, it will now be possible to target these genes more specifically and interrupt its life cycle.