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Page "Outerplanar graph" ¶ 11
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Every and outerplanar
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 outerplanar graph is also a subgraph of a series-parallel graph.
Every forest, and every cactus graph is outerplanar.
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 maximal outerplanar graph is the visibility graph of a simple polygon.
Every outerplanar graph is a circle graph, the intersection graph of a set of chords of a circle.
Every outerplanar graph can be represented as an intersection graph of axis-aligned rectangles in the plane, so outerplanar graphs have boxicity at most two.

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 tree is a bipartite graph and a median graph.
Every tree with only countably many vertices is a planar graph.
* 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 connected graph with only countably many vertices admits a normal spanning tree.
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 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 planar graph whose faces all have even length is bipartite.
Every vertex of this graph has an even degree, therefore this is an Eulerian graph.
Every Eulerian orientation of a connected graph is a strong orientation, an orientation that makes the resulting directed graph strongly connected.

Every and is
Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every single problem touched on thus far is related to good marketing planning.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every man in every one of these houses is a Night Rider.
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.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Every infinite game in which is a Borel subset of Baire space is determined.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

Every and planar
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 .
Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.
Every movement she made seemed unnecessarily noisy.
`` Every last one of you.
Every plane that could fly was sent into the air.
Every so often the diminishing sound of a car came under the trailer as it slowed down for the wreck then speeded up again as it got clear.
Every so often he turned the knife.
Every bone and muscle in his body showed, but he did not give the appearance of starving.
Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.
Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.
Every slight sound that rose against that pressure fell away again, crushed beneath it.
They give strict interpretation to William James' statement that `` Every idea that enters the mind tends to express itself ''.
Every morning contingents of prisoners would be sent out to labor in nearby factories.
If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.
Every day, when the President took his nap, Rob Roy would stretch out on the window seat near him, like a perfect gentleman, and stare thoughtfully out the window, or he would take a little nap himself.
Every First Family seems to have one couple upon whom it relies for true friendship.
Every letter answers itself in a couple of weeks ''.
Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.
Every chance I got I left the hotel to visit Lilly.
Every man who dabbles in the market to make a little easy money on the side and suffers losses could at the time hardly face his wife who was wondering how her husband could be so dumb.
Sir -- Every resident of this city should visit the Newark Museum and see the exhibit `` Our Changing Skyline in Newark ''.
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every eye was on him as he began to speak.
Every time he moved or said something, the chair creaked again.

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