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 carved from natural crystalline stone ( such as quartz, beryl, calcite, obsidian, or amethyst ), it may display the natural coloring and structure of the mineral from which it was fashioned.

If the algorithm terminates without finding an odd cycle in this way, then it must have found a proper coloring, and can safely conclude that the graph is bipartite.

If, on the other hand, the doubled vertex does not belong to a maximum clique, form a graph H by removing the vertices with the same color as the doubled vertex ( but not the doubled vertex itself ) from an optimal coloring of the given graph.

If one further required that each node must be active continuously for 1 time unit ( without switching it off and on every now and then ), then traditional graph vertex coloring would provide an optimal schedule: first the nodes of color 1 are active for 1 time unit, then the nodes of color 2 are active for 1 time unit, and so on.

Furthermore, when a horse is homozygous for Tobiano coloring, all of that horse's offspring will be spotted, with only a few exceptions: If either parent passes the dominant gray gene to the foal, then its spots will be visible while it is young, but will gradually become lighter until finally, as the gray gene acts upon all coat colors, the entire horse's coat fades.

If the city council fails to consider appointment of a full-time CD director, Mr. Hawksley said, then he plans to call a meeting early in September so that a civil defense organization will be developed locally.

If it fails to pass, he can throw up his hands and say the Legislature would not support him in his efforts to prevent integration.

If a single test fails, then the theory is falsified.

If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist.

If the bankrupt fails to lodge the document within a certain period of time, he or she can be prosecuted and fined.

If the bankrupt fails to pay the contributions due, the trustee can issue a notice to garnishee the bankrupt's wages.

If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.

* If the offence fails to make ten yards in three plays, the defence takes over on downs.

* If the offence fumbles ( a ball carrier drops the football, or has it dislodged by an opponent, or if the intended player fails to catch a lateral pass or a snap from centre, or a kick attempt is blocked by an opponent ), the ball may be recovered ( and advanced ) by either team.

He is still seeking greater autonomy from China, although Dolma Gyari, deputy speaker of the parliament-in-exile has stated " If the middle path fails in the short term, we will be forced to opt for complete independence or selfdetermination as per the UN charter ".

If the Dance Gauge is fully depleted during gameplay, the player fails the song, usually resulting in a game over.

< tr >< td > If variolation after infection with cowpox fails to produce a smallpox infection, immunity to smallpox has been achieved.

If power fails, all essential equipment will run off huge batteries for up to 20 minutes, during which time four one-megawatt diesel generators will take over.

If the implementation of the change should fail or, the post implementation testing fails or, other " drop dead " criteria have been met, the back out plan should be implemented.

If this continues far enough, the working end passes into the knot and the knot unravels and fails.

If a team does not attempt to score a field goal ( or the ball fails to make contact with the rim ) within 24 seconds of obtaining the ball, play is stopped and the ball given to its opponent.

If the egg fails to release from the follicle in the ovary an ovarian cyst may form.

If a player fails to make the contract and takes overtrick ( s ), he / she scores the number of tricks taken.

If he fails on the turn, he then has a 9 / 46 chance to fill on the river.

If any goal fails in the course of executing the program, all variable bindings that were made since the most recent choice-point was created are undone, and execution continues with the next alternative of that choice-point.

If this fails then watermark fluid may be used, which " wets " the stamp to reveal the mark.

If the vaulter fails to begin an attempt within this time, the vaulter is charged with a time foul and the attempt is a miss.

If one peer on the network fails to function properly, the whole network is not compromised or damaged.

If the child drops the gun and it breaks someone's foot, the HWR test fails, as a broken foot was not the type of harm anticipated.

If the visitor fails to do so, usually a quarantine fine of 220 Australian dollars are to be paid as quarantine infringement notice, and if not, the visitor may face criminal convictions of fining 100, 000 Australian dollars and 10 years imprisonment.

If you take the one, you'd better take both ''.

`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.

If one dancer slaps another, the victim may do a pirouette, sit down, or offer his assailant a fork and spoon.

If a child had a single drop of Negro blood, he would revert to the ancestral line which, except as slaves under a superior race, had not made one step of progress in 3,000 years.

If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.

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 within one year you can make a success out of the American, you can practically name your own salary thereafter.

If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.

If one finger is raised against the authorities, all our moral power will vanish.

If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.

If he can bounce back with one of those 25 home runs years, the club will have to be better off offensively.

If they do meet and recognize one another, slap backs and embrace, the moment soon is done.

If either one ever started making promises, there is no telling where the promises would end.

If one follows the reports of the Congress, one finds that there still seems considerable uncertainty in the minds of the leaders themselves about what exactly to do in this matter.

Somebody, got to be somebody If I don't put my two cents in soon, somebody else will I know they're waitin only for one thing: for the bastards what done it to be nailed.

If we had, then one of us would have had to go instead.

`` If I catch you one more time down here without stockings '' --

If, for some reason such as economy, we are not going to develop aircraft nuclear propulsion with a sense of national urgency, then we should turn our effort to developing jet engines with a thrust-to-weight ratio of 12 or 15 to one.

If you don't own a planer and don't want to buy one, it's well worth renting.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

If you have a full-time doctor now, can he be replaced with a part-time doctor or one who serves on a fee-per-case basis only??

If you use one of the new year-round cooling system fluids such as `` Dowguard '' be sure to check it.

If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.