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Page "Bipartite graph" ¶ 25
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If and when
If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.
If I hadn't got Nate stopped when I did, my duds'd all be shot plumb to hell!!
`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.
If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.
If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.
If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.
If they give him advice when he asks it, or if they perform specified duties under his direction, the nature of the U. N. will not of necessity change.
Mr. Richard Preston, executive director of the New Hampshire State Planning and Development Commission, in his remarks to the Governors Conference on Industrial Development at Providence on October 8, 1960, warned against the fallacy of attempting to attract industry solely to reduce the tax rate or to underwrite municipal services such as schools when he said: `` If this is the fundamental reason for a community's interest or if this is the basic approach, success if any will be difficult to obtain ''.
If the world comes to this, wouldn't it be the very time when courage and American know-how would be needed to help survivors rebuild??
If Simms Purdew would turn to him and say: `` Adam, you know when I was a boy, it was a funny thing happened.
If and when Hino decided to tell him about his experiences, he would do so unasked.
If you have a 6- to 8-inch drain pipe, you may easily wash out all the debris when the grate is out.
If you can't see your way clear to have summer cooling included when building, by all means make provision for its easy adding later.
If private brand competition hasn't been felt in your product field as yet, have you thought how you will cope with it if and when it does appear??
`` If you saw the drama called Rhinoceros '', I said, `` think of the effect it would have on an audience of rhinos when the actor on stage suddenly begins turning into a rhinoceros.
If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.
If each text form is marked when matched with a dictionary form, the text forms not contained in the dictionary can be identified when all dictionary forms have been read.
If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.
If you look at a reading meant for someone else, you will probably see that many of the items could be considered as applicable to you, even when you were not in the picture at all!!
If you are going to farm for extra cash income on a part-time basis you must keep in mind the needed machinery investments when you choose among farm enterprises.
Chief Moore said, `` If I don't see you when I return, see you for certain at my road block, Inspector ''.
If I could put your body in an imaginary atomic press and squeeze you down, squeeze these holes out of you in the way we squeeze the holes out of a sponge, you would get smaller and smaller until finally when the last hole was gone, you would be smaller than the smallest speck of dust that you could see on this piece of paper.
If elements in the sample space increase arithmetically, when placed in some order, then the median and arithmetic average are equal.

If and vertex
If the vertex is at Af, and if the interior of C is on the left as one moves in the direction of increasing t, then every such corner can be found from the curve obtained by rotating C clockwise through 90-degrees about the vertex.
If v < sub > n </ sub > is the number of vertices of degree n and D is the maximum degree of any vertex,
If there is a graph requiring 5 colors, then there is a minimal such graph, where removing any vertex makes it four-colorable.
If there is an edge from a vertex x to a vertex y, then the element is 1 ( or in general the number of xy edges ), otherwise it is 0.
If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other.
If the polar vertex is " pulled down " 90 °, so that the vertex is on the equator, or transverse diameter, then it becomes the transverse graticule, upon which all spherical trigonometry is ultimately based ( if the longitudinal vertex is between the poles and equator, then it is considered an oblique graticule ).
If this fragment is part of a larger graph, then any Hamiltonian cycle through the graph must go in or out of the top vertex ( and either one of the lower ones ).
If loops are permitted, then the graph with a single vertex and one loop is terminal.
If at any step a vertex has ( visited ) neighbours with the same label as itself, then the graph is not bipartite.
If n is odd each axis of symmetry connects the midpoint of one side to the opposite vertex.
For example, given a graph G =( V, E ), the shortest path p from a vertex u to a vertex v exhibits optimal substructure: take any intermediate vertex w on this shortest path p. If p is truly the shortest path, then the path p < sub > 1 </ sub > from u to w and p < sub > 2 </ sub > from w to v are indeed the shortest paths between the corresponding vertices ( by the simple cut-and-paste argument described in CLRS ).
If G is a connected graph with infinitely many vertices such that every vertex has finite degree ( that is, each vertex is adjacent to only finitely many other vertices ) then G contains an infinitely long simple path, that is, a path with no repeated vertices.
If one angle is a right angle, the orthocenter coincides with the vertex of the right angle.
If I needed a bit of colour, I'd add it in the vertex.
If there are no negative-weight cycles, then every shortest path visits each vertex at most once, so at step 3 no further improvements can be made.
If the edges of a graph are thought of as lines drawn from one vertex to another ( as they are usually depicted in illustrations ), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if they are homeomorphic in the sense in which the term is used in topology.

If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

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