[permalink] [id link]

Conversely any planar graph can be formed from a map in this way.

from
Wikipedia

## Some Related Sentences

Conversely and any

__Conversely__,

**a**subset R defines

**a**binary function if and only if, for

__any__x

**in**X and y

**in**Y, there exists

**a**unique z

**in**Z such that ( x, y, z ) belongs to R

**.**

__Conversely__the equilibrium position is said to

**be**" far to the left " if hardly

__any__product is

**formed**

**from**the reactants

**.**

* The spectrum of

__any__bounded linear operator on**a**Banach space is**a**nonempty compact subset of the complex numbers C**.**__Conversely__,__any__compact subset of C arises**in****this**manner, as the spectrum of some bounded linear operator**.**__Conversely__, there are other stars that never rise above the horizon, as seen

**from**

__any__given point on the Earth's surface ( except exactly on the equator ).

__Conversely__,

__any__surjection between sets determines

**a**partition on its domain, the set of preimages of singletons

**in**the codomain

**.**

__Conversely__, Derek Bickerton and others argue that the advent of abstract words provided

**a**mental basis for analyzing higher-order relations, and that

__any__communication system that remotely resembles human language utterly relies on cognitive architecture that co-evolved alongside language

**.**

__Conversely__,

**a**person may feel like he belongs to one state without having

__any__legal relationship to it

**.**

__Conversely__, the interior of the box has

**a**constant, zero potential energy .< ref > Actually,

__any__constant, finite potential

**can**

**be**specified within the box

**.**

__Conversely__, extremely thin jewelry

**can**cause the same tearing

**in**what is commonly referred to as the " cheese cutter effect ", either during sudden torsion or over

**a**long period of wearing, especially if the thin jewelry bears

__any__weight

**.**

__Conversely__,

__any__Hermitian positive semidefinite matrix M

**can**

**be**written as M = A < sup >*</ sup > A ;

**this**is the Cholesky decomposition

**.**

__Conversely__, if

**a**double sharp were added to

__any__other note not containing

**a**sharp or flat as indicated by the key signature then the note will

**be**raised two semitones or

**a**whole step with respect to the chromatic scale

**.**

__Conversely__, supplementation with L-phenylalanine, L-tyrosine, L-DOPA, or

__any__of the cofactors will increase their respective concentrations

**.**

__Conversely__,

__any__choice of μ, full rank matrix U, and positive diagonal entries Λ < sub > i </ sub > yields

**a**non-singular multivariate normal distribution

**.**

__Conversely__, the influence of the data at

__any__given point on the initial line propagates with the finite velocity c: there is no effect outside

**a**triangle through that point whose sides are characteristic curves

**.**

__Conversely__, given

__any__harmonic function

**in**two dimensions, it is the real part of an analytic function, at least locally

**.**

__Conversely__, if the Turing Machine is expected polynomial-time ( for

__any__given x ), then

**a**considerable fraction of the runs must

**be**polynomial-time bounded, and the coin sequence used

**in**such

**a**run will

**be**

**a**witness

**.**

It is

**a**fact that the ring is**a**principal ideal ring ; that is, for__any__ideal I**in**, there exists an integer n**in**I such that every element of I is**a**multiple of n**.**__Conversely__, the set of all multiples of an arbitrary integer n is necessarily an ideal, and is usually denoted by ( n ).

Conversely and planar

__Conversely__, given an ordered tree, and conventionally draw the root at the top, then the child nodes

**in**an ordered tree

**can**

**be**drawn left-to-right, yielding an essentially unique

__planar__embedding ( up to embedded homotopy, i

**.**e., moving the edges and nodes without crossing ).

Conversely and graph

__Conversely__, every preorder is the reachability relationship of

**a**directed

__graph__( for instance, the

__graph__that has an edge

**from**x to y for every pair ( x, y ) with x ≤ y ).

__Conversely__, if R is

**a**symmetric relation over

**a**set X, one

**can**interpret it as describing an undirected

__graph__with the elements of X as the vertices and the pairs

**in**R as the edges

**.**

A hypergraph H may

**be**represented by**a**bipartite__graph__BG as follows: the sets X and E are the partitions of BG, and ( x < sub > 1 </ sub >, e < sub > 1 </ sub >) are connected with an edge if and only if vertex x < sub > 1 </ sub > is contained**in**edge e < sub > 1 </ sub >**in**H**.**__Conversely__,**any**bipartite__graph__with fixed parts and no unconnected nodes**in**the second part represents some hypergraph**in**the manner described above**.**__Conversely__,

**any**median

__graph__

**can**

**be**represented as the set of solutions to

**a**2-satisfiability instance

**in**

**this**

**way**

**.**

__Conversely__, as Lefschetz shows, whenever

**a**

__graph__G has

**a**set of cycles with

**this**property, they necessarily form the face cycles of an embedding of the

__graph__onto the sphere

**.**

__Conversely__

**any**bipartite

__graph__with girth at least six

**can**

**be**viewed as the Levi

__graph__of an abstract incidence structure

**.**

__Conversely__, the histogram for

**a**very bright image with few dark areas and / or shadows will have most of its data points on the right side and center of the

__graph__

**.**

To

**a**__graph__G there corresponds**a**signed complete__graph__Σ on the same vertex set, whose edges are signed negative if**in**G and positive if not**in**G**.**__Conversely__, G is the subgraph of Σ that consists of all vertices and all negative edges**.**

Conversely and can

__Conversely__, if

**a**Boolean ring A is given, we

__can__turn it into

**a**Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y

**.**

__Conversely__,

**in**the English language as

**a**whole, singular verb forms

__can__often

**be**used with nouns ending

**in**"- s " that were once considered plural ( for example: " Physics is my favorite academic subject ").

__Conversely__, every point on the line

__can__

**be**interpreted as

**a**number

**in**an ordered continuum which includes the real numbers

**.**

__Conversely__, non-spontaneous electrochemical reactions

__can__

**be**driven forward by the application of

**a**current at sufficient voltage

**.**

__Conversely__, badly managed food aid

__can__create problems by disrupting local markets, depressing crop prices, and discouraging food production

**.**

__Conversely__, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity

__can__

**be**reduced to O ( K log N log ( N / K )), and

**this**has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32

**in**

**a**large-N example ( N = 2 < sup > 22 </ sup >) using

**a**probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

__Conversely__, when one wants to compute an arbitrary number ( N ) of discrete samples of one cycle of

**a**continuous DTFT, it

__can__

**be**done by computing the relatively simple DFT of s < sub > N </ sub >, as defined above

**.**

__Conversely__, rifle bullets

__can__pierce light armor and are easier to shoot accurately, but even

**a**carbine such as the Colt M4 is larger and / or longer than

**a**submachine gun, making it harder to maneuver

**in**close quarters

**.**

__Conversely__, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces ( such as electromagnetism or friction ),

__can__

**be**used to define the geometry of space, as well as

**a**time coordinate

**.**

__Conversely__,

**a**high pH, low CO < sub > 2 </ sub >, or low 2, 3 BPG favors the relaxed form which

__can__better bind oxygen

**.**

__Conversely__,

**a**very severe bit,

**in**the right hands,

__can__transmit subtle commands that cause no pain to the horse

**.**

Given

**a**field ordering ≤ as**in**Def 1, the elements such that x ≥ 0 forms**a**positive cone of F**.**__Conversely__, given**a**positive cone P of F as**in**Def 2, one__can__associate**a**total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P**.**This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1**.**__Conversely__, every formally real field

__can__

**be**equipped with

**a**compatible total order, that will turn it into an ordered field

**.**

__Conversely__, if the odds of drawing

**a**winning card are numerically lower than the pot odds, the call has

**a**negative expectation, and you

__can__expect to win less money on average than it costs to call the bet

**.**

__Conversely__,

**from**

**a**partial order on

**a**partition of

**a**set S one

__can__construct

**a**preorder on S

**.**There is

**a**1-to-1 correspondence between preorders and pairs ( partition, partial order ).

__Conversely__we have

**a**b if and only if

**a**< b or

**a**~ b

**.**This is the reason for using the notation ""; "≤"

__can__

**be**confusing for

**a**preorder that is not anti-symmetric, it may suggest that

**a**≤ b implies that

**a**< b or

**a**

__Conversely__, though every president

**from**Washington to John Quincy Adams

__can__

**be**definitely assigned membership

**in**an Anglican or Unitarian body, the significance of these affiliations is often downplayed as unrepresentative of their true beliefs

**.**

__Conversely__, specifying the symmetry

__can__define the structure, or at least clarify what we mean by an invariant, geometric language

**in**which to discuss it ;

**this**is one

**way**of looking at the Erlangen programme

**.**

__Conversely__, water deep

**in**the ocean near geothermal vents

__can__reach temperatures of hundreds of degrees and remain liquid

**.**

__Conversely__, AES is sensitive to the lighter elements, and unlike X-ray fluorescence, Auger peaks

__can__

**be**detected for elements as light as lithium ( Z = 3 ).

0.310 seconds.