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Page "Hypergraph" ¶ 56
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If and all
He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.
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 Blue Throat has his way he'll keep us all cooped up in here for days '', he said.
If communications work, his decision would be instantly known in all command posts that would originate the actual go order.
If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.
If there were only darkness, all would be clear.
If there were only the mess, all would be clear ; ;
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 in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.
If one finger is raised against the authorities, all our moral power will vanish.
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 once they become inattentive to the public affairs '', Jefferson said, `` you and I, and Congress and assemblies, judges and governors, shall all become wolves ''.
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If the President of the United States really feels he won himself a `` lousy job '', then heaven help us all.
If we go all gooey over this newest Castro ( until he proves he isn't ) we've got rocks in our heads.
`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.
If we grasp this orientation as a key, our national conduct in all of the events here mentioned becomes intelligible.
If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.
If Joe doesn't show up, we'll all be back here at 0600 hours.
If we could use all the small airfields we have in this country, we could disperse our strategic aircraft by a factor of 10 or more.
If the points aren't thrown all the way, the Turnout cannot be locked, and in turn, the signal cannot be cleared.
If you have a 6- to 8-inch drain pipe, you may easily wash out all the debris when the grate is out.

If and edges
If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.
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 cutting tools were not used, individual stamps were torn off, as evidenced by the ragged edges of surviving such examples.
* If leather on the side of a shoe is scored by several parallel cuts, it was caused by someone who scraped around the edges of the sole in order to remove crusted mud.
If all three pairs of opposite edges of a tetrahedron are perpendicular, then it is called an orthocentric tetrahedron.
If the wipe proceeds from two opposite edges of the screen toward the center or vice versa, it is known as a barn door wipe ( named for its similarity to a pair of doors opening or closing ).
If a piece is placed that creates a connection between both players ' goal edges ( i. e. all edges are connected ), the winner is the player who placed the final piece.
If Keen narrowly misses a jump, he can grab onto the edges of most platforms, and climb up.
If the beam does not fill more than a third of the beam profiler ’ s sensor area, then there will be a significant number of pixels at the edges of the sensor that register a small baseline value ( the background value ).
If the baseline value is large or if it is not subtracted out of the image, then the computed D4σ value will be larger than the actual value because the baseline value near the edges of the sensor are weighted in the D4σ integral by x < sup > 2 </ sup >.
If there are n vertices in the graph, then each tree has n-1 edges.
If the mirrors have vertical edges then the left edge of the field of view is the plane through the right edge of the first mirror and the edge of the second mirror which is on the right when looked at directly, but on the left in the mirror image.
If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a simple cycle, circuit, circle, or polygon ; see Cycle graph.
If the cut edges did not align correctly or the gluing was not done well, there might still be water leakage along the seam.
) If any of the edges ( r, s ), ( r, t ), ( s, t ) are also blue then we have an entirely blue triangle.
If not, then those three edges are all red and we have an entirely red triangle.
If this is done in such a way that, when glued together, neighboring edges are pointing in the opposite direction, then this determines an orientation of the surface.
If we have 2 nodes with an odd number of edges, the walk must begin at one such node and end at the other.
If U, V, W, u, v, w are lengths of edges of the tetrahedron ( first three form a triangle ; u opposite to U and so on ), then
However, many different DAGs may give rise to this same reachability relation: for example, the DAG with two edges a → b and b → c has the same reachability as the graph with three edges a → b, b → c, and a → c. If G is a DAG, its transitive reduction is the graph with the fewest edges that represents the same reachability as G, and its transitive closure is the graph with the most edges that represents the same reachability.
If a DAG G represents a partial order ≤, then the transitive reduction of G is a subgraph of G with an edge u → v for every pair in the covering relation of ≤; transitive reductions are useful in visualizing the partial orders they represent, because they have fewer edges than other graphs representing the same orders and therefore lead to simpler graph drawings.

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