* 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 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 is related to itself via two length-zero paths, which are identical but nevertheless edge-disjoint.

# 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 room has the following: air conditioning-telephone-radio-Beauty Rest box springs and mattresses-private baths.

Every individual can simply place all of their trash back into the box or bag to clean up.

Every crew will consist of a referee, who is generally in charge of the game and watches action on the quarterback and in the offensive backfield ; an umpire, who handles spotting the ball and watches action on the offensive line ; and a head linesman, who supervises placement of the down box and line-to-gain chains.

Every soldier equipped with the Sig 550 assault rifle used to be issued 50 rounds of ammunition in a sealed box, to be opened only upon alert.

Jonathan Cain sings lead on " Every Generation ", the first time he sang lead since " All That Really Matters " ( a song originally left off Frontiers ) from the Time < sup > 3 </ sup > box set.

Every Irish mobile number has a corresponding voicemail box number.

Every page of the website features a “ What Film ?” box, which randomly selects one of the many thousands of reviews.

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 connected graph is an expander ; however, different connected graphs have different expansion parameters.

Every individual is connected with the rest of the world, and the universe is fashioned for universal harmony.

Every aspect of life, every word, plant, animal and ritual was connected to the power and authority of the gods.

* Every connected graph with only countably many vertices admits a normal spanning tree.

Every aspect of life, every word, plant, animal and ritual was connected to the power and authority of the gods.

Every device connected to one of its ports can send packets to any of the others.

The generalized Poincaré conjecture states that Every simply connected, closed n-manifold is homeomorphic to the n-sphere.

Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).

Every part of it, including the blue and white colors ( see below ), the cross, as well as the stripe arrangement can be connected to very old historical elements ; however it is difficult to establish " continuity ", especially as there is no record of the exact reasoning behind its official adoption in early 1822.

Every Eulerian orientation of a connected graph is a strong orientation, an orientation that makes the resulting directed graph strongly connected.

Every broadcasting company has members and the number of members gives them a status that is connected to the number of hours of broadcasting.

Every graph ( that is connected and not a tree ) has multiple spanning trees, so we once again have an example where the problem itself allows multiple possible outcomes, and the algorithm chosen can arrive at any one of them, but will never arrive at something else.

This flat may be identified with the partition of the vertices of into the connected components of the subgraph formed by: Every set of edges having the same closure as gives rise to the same partition of the vertices, and may be recovered from the partition of the vertices, as it consists of the edges whose endpoints both belong to the same set in the partition.

Every rational variety, including the projective spaces, is rationally connected, but the converse is false.

* Every external device connected to the Freebox player is available to that device only but the devices connected to the Freebox Server are available to every Freebox player connected.

Every extra foot of cord increases the electrical resistance, which decreases the power the cord can deliver to connected devices.

Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere.

Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree.