* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

Every vertex in a polygon is assigned a texture coordinate ( which in the 2d case is also known as a UV coordinate ) either via explicit assignment or by procedural definition.

Every vertex of this graph has an even degree, therefore this is an Eulerian graph.

Every maximal outerplanar graph satisfies a stronger condition than Hamiltonicity: it is node pancyclic, meaning that for every vertex v and every k in the range from three to the number of vertices in the graph, there is a length-k cycle containing v. A cycle of this length may be found by repeatedly removing a triangle that is connected to the rest of the graph by a single edge, such that the removed vertex is not v, until the outer face of the remaining graph has length k.

Every vertex of an-dimensional box is connected to edges.

Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color ; thus χ < sub > H </ sub >( G ) ≤ | V ( G )|.

Every triangle has exactly three medians: one running from each vertex to the opposite side.

# Every vertex in G either belongs to D or is adjacent to a vertex in D. That is, D is a dominating set of G.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial.

Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.

* PASSIA Diaries and Annual Reports: Every year since 1988, PASSIA publishes its “ Diary ”, a unique annual resource book combining a comprehensive directory of contact information for Palestinian and interna tional institu tions operating in Palestine, a day-to-day calendar, and an agenda containing facts and figures, graphs, statistics, chronologies and maps related to Palestine and the Palestinians.

Every base he closed resulted in a new construction project elsewhere to expand another base, relocation of forces projects and other related spending.

One unique challenge that the team encountered early on was related to deph perception, the team remedied through the use of shadows: Every object in the game has a shadow directly below it regardless of the area's lighting.

Every enterprise constrains behavior in some way, and this is closely related to constraints on what data may or may not be updated.

Every object related to Flipje has become a collector's item in the Netherlands.

Every territorial force has a specialist Firearms Unit, which maintains Armed Response Vehicles to respond to firearms related emergency calls, while one territorial force ( the Police Service of Northern Ireland ) and two of the special police forces, ( the Civil Nuclear Constabulary and the Ministry of Defence Police ) are routinely armed.

Every foreign key must be joined to see the related data item.

Partially as a response to this, Dyer published a collection of his articles on the Middle East and related topics called With Every Mistake in 2005.

Every class prepares a float which corresponds with the Homecoming theme or related theme of school spirit as assign by school administrators.

Every part of a Gothic cathedral is directly related to a “ core dimension ” which is used as an effort to achieve harmony and organic unity within the building where everything is linked rationally and proportionally, creating a coherent whole.

" Gender equity " is one of the goals of the United Nations Millennium Project, to end world poverty by 2015 ; the project claims, " Every single Goal is directly related to women's rights, and societies where women are not afforded equal rights as men can never achieve development in a sustainable manner.

Every working group gets a camera and has to shoot a short film related to the topic for one day.

Every member of a lakinyeri is related by blood and it is forbidden to marry any member of the same lakinyeri.

Every orthogonal transformation of a k-frame in R < sup > n </ sup > results in another k-frame, and any two k-frames are related by some orthogonal transformation.

Every living thing was related in a branching pedigree, not ascending a Lamarckian ladder, and this pedigree was the proper basis for classification.

Every spring, CPILJ hosts a symposium on important issues related to public interest law.

Every week on Xbox Live, Major's Minute recaps new content and news related to the Xbox Live Marketplace.

Every Val has a bloodline, which is tied to a specific god ; they are gifted with divine powers which they may improve ; these are related to their bloodline.

Every year, numerous festivals are held through the Appalachian region, and throughout the world, to celebrate Appalachian music and related forms of music.