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

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## Some Related Sentences

Every and connected

__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**G

**admits**

**a**

**spanning**

**tree**, which is

**a**

**tree**that contains every vertex of G and whose edges are edges of G

**.**

__Every__aspect of life, every word, plant, animal and ritual was

__connected__to the power and authority of the gods

**.**

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__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__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

**.**

Every and graph

:"[...]

__Every__invariant and co-variant thus becomes expressible by**a**__graph__precisely identical**with****a**Kekuléan diagram or chemicograph**.**
In mathematics, Tait's conjecture states that "

__Every__3-connected planar cubic__graph__has**a**Hamiltonian cycle ( along the edges ) through all its**vertices**".__Every__homomorphism of the Petersen

__graph__to itself that doesn't identify adjacent

**vertices**is an automorphism

**.**

__Every__directed acyclic

__graph__has

**a**topological ordering, an ordering of the

**vertices**such that the starting endpoint of every edge occurs earlier in the ordering than the ending endpoint of the edge

**.**

__Every__maximal outerplanar

__graph__

**with**n

**vertices**has exactly 2n − 3 edges, and every bounded face of

**a**maximal outerplanar

__graph__is

**a**triangle

**.**

Every and with

__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__Wednesday night through Oct. 11 there will be an elaborate colored fountain display,

__with__229 nozzles throwing jets of water up to 130 feet

**.**

** Tukey's lemma:

__Every__non-empty collection of finite character has**a**maximal element__with__respect to inclusion**.**__Every__unit of length has

**a**corresponding unit of area, namely the area of

**a**square

__with__the given side length

**.**

*****Revised Code of Washington 9

**.**12

**.**010: "

__Every__person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state,

__with__intent thereby to distress or harass

**a**defendant in the suit, or who serves or sends any paper or document purporting to be or resembling

**a**judicial process, that is not in fact

**a**judicial process, is guilty of

**a**misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state

**.**

__Every__Boolean algebra ( A, ∧, ∨) gives rise to

**a**ring ( A, +, ·) by defining

**a**+ b := (

**a**∧ ¬ b ) ∨ ( b ∧ ¬

**a**) = (

**a**∨ b ) ∧ ¬(

**a**∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and

**a**· b :=

**a**∧ b

**.**The zero element of this ring coincides

__with__the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra

**.**

__Every__Hilbert space X is

**a**Banach space because, by definition,

**a**Hilbert space is complete

__with__respect to the norm associated

__with__its inner product, where

**a**norm and an inner product are said to be associated if for all x ∈ X

**.**

*****

__Every__quadratic Bézier curve is also

**a**cubic Bézier curve, and more generally, every degree n Bézier curve is also

**a**degree m curve for any m > n

**.**In detail,

**a**degree n curve

__with__control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve

__with__control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where

**.**

*****

__Every__unital real Banach algebra

__with__no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions

**.**

*****

__Every__commutative real unital Noetherian Banach algebra

__with__no zero divisors is isomorphic to the real or complex numbers

**.**

Jimmy Hatlo's They'll Do It

__Every__Time was often displayed in**a**two-panel format__with__the first panel showing some deceptive, pretentious, unwitting or scheming human behavior and the second panel revealing the truth of the situation**.**__Every__year, the European Joint Conferences on Theory and Practice of Software ( ETAPS ) sponsors the International Conference on Compiler Construction ( CC ),

__with__papers from both the academic and industrial sectors

**.**

According to

__Every__, one example may be " the myth of St**.**George " and other stories about saints battling dragons, which were " modelled no doubt in**many**cases on older representations of the creator and preserver of the world in combat__with__chaos ".*****

__Every__three years since Earnhardt's death, someone associated

__with__Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr

**.**in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010

**.**

In Norse mythology, Draupnir ( Old Norse " the dripper ") is

**a**gold ring possessed by the god Odin__with__the ability to multiply itself:__Every__ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original**.**__Every__system must have

**a**class designated as " root ",

__with__one of its creation procedures designated as " root procedure ".

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