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* Every planar graph whose faces all have even length is bipartite.

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## Some Related Sentences

Every and planar

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__

__planar__

**graph**has a flat and linkless embedding: simply embed the

**graph**into a plane and embed the plane into space

**.**

__Every__second, approximately 6, 000

__planar__cross-sections of a 3D volume are projected onto a spinning diffuser in the Perspecta volumetric 3D display ( made by the former Actuality Systems, Inc .).

__Every__

__planar__

**graph**has an algebraic dual, which

**is**in general not unique ( any dual defined by a plane embedding will do ).

Every and graph

__Every__connected

__graph__

**is**an expander ; however, different connected graphs

**have**different expansion parameters

**.**

:"[...]

__Every__invariant and co-variant thus becomes expressible by a__graph__precisely identical with a Kekuléan diagram or chemicograph**.*******

__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__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__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__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 whose

__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

**.**

Group actions / representations:

__Every__group G can be considered as a category with a single object__whose__morphisms are the elements of G**.**A functor from G to Set**is**then nothing but a group action of G on a particular set, i**.**e**.**a G-set**.**__Every__field theory of particle physics

**is**based on certain symmetries of nature

__whose__existence

**is**deduced from observations

**.**

__Every__cycle climaxes in the arrival of The Leveler,

__whose__approach ( and fall )

**is**heralded by an ominous comet that appears in the sky

**.**

__Every__rational number / has two closely related expressions as a finite continued fraction,

__whose__coefficients can be determined by applying the Euclidean algorithm to

**.**

__Every__congruence relation has a corresponding quotient structure,

__whose__elements are the equivalence classes ( or congruence classes ) for the relation

**.**

__Every__morphism in a concrete category

__whose__underlying function

**is**injective

**is**a monomorphism ; in other words, if morphisms are actually functions between sets, then any morphism which

**is**a one-to-one function will necessarily be a monomorphism in the categorical sense

**.**

__Every__family head in the Mafia selects a man

__whose__characteristics already make him look approachable

**.**

*****

__Every__root of a monic polynomial

__whose__coefficients are algebraic integers

**is**itself an algebraic integer

**.**

__Every__polynomial in can be factorized into polynomials that are irreducible over F

**.**This factorization

**is**unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field

**is**a unique factorization domain

__whose__units are the nonzero constant polynomials ).

She was raised there by her mother, Ellen Simmons,

__whose__Sioux name was Taté Iyòhiwin (__Every__Wind or Reaches for the Wind ).*****

__Every__Parliament constituted in conformity with the laws of a sovereign State

__whose__population it represents and on

__whose__territory it functions may request affiliation to the Inter-Parliamentary Union

**.**

" A man's home

**is**his castle "**is**translated in Gor as, "__Every__man**is**an Ubar within the circle of his sword " ( The Ubar**is**a war-leader, a General who takes power at a time of crisis, and__whose__rule**is**tantamount to tyrant until the crisis**is**resolved**.**
During this period he lived with the French poet Pierre Martory,

__whose__books__Every__Question but One ( 1990 ), The Landscape Is behind the door ( 1994 ) and The Landscapist he has translated ( 2008 ), as he has Jean Perrault ( Camouflage ), Max Jacob ( The Dice Cup ), Pierre Reverdy and Raymond Roussel**.**__Every__governor since Ronald Reagan in 1968 has been subject to a recall effort, but Gray Davis was the first governor

__whose__opponents gathered the necessary signatures to qualify for a special election

**.**

__Every__artist she showed the script to had declined to take on the project, so it was offered to aspiring artist Arthur Adams,

__whose__samples had been given to editor Carl Potts and Nocenti, his assistant editor, by editor Al Milgrom

**.**

*****

__Every__integrable subbundle of the tangent bundle — that

**is**, one

__whose__sections are closed under the Lie bracket — also defines a Lie algebroid

**.**

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