Every tree with only countably many vertices is a planar graph.

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 outerplanar graph is a planar graph.

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 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 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.

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 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 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 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 root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

# Every sequence in A has a convergent subsequence, whose limit lies in A.

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.

Every cycle climaxes in the arrival of The Leveler, whose approach ( and fall ) is heralded by an ominous comet that appears in the sky.

Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.

Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes ( or congruence classes ) for the relation.

Every morphism in a concrete category whose underlying function is injective is a monomorphism ; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily be a monomorphism in the categorical sense.

Every morphism in a concrete category whose underlying function is surjective is an epimorphism.

Every family head in the Mafia selects a man whose characteristics already make him look approachable.

* Every root of a monic polynomial whose coefficients are algebraic integers is itself an algebraic integer.

Every polynomial in can be factorized into polynomials that are irreducible over F. This factorization is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the ring of polynomials over a field is a unique factorization domain whose units are the nonzero constant polynomials ).

She was raised there by her mother, Ellen Simmons, whose Sioux name was Taté Iyòhiwin ( Every Wind or Reaches for the Wind ).

* Every Parliament constituted in conformity with the laws of a sovereign State whose population it represents and on whose territory it functions may request affiliation to the Inter-Parliamentary Union.

" A man's home is his castle " is translated in Gor as, " Every man is an Ubar within the circle of his sword " ( The Ubar is a war-leader, a General who takes power at a time of crisis, and whose rule is tantamount to tyrant until the crisis is resolved.

During this period he lived with the French poet Pierre Martory, whose books Every Question but One ( 1990 ), The Landscape Is behind the door ( 1994 ) and The Landscapist he has translated ( 2008 ), as he has Jean Perrault ( Camouflage ), Max Jacob ( The Dice Cup ), Pierre Reverdy and Raymond Roussel.

Every governor since Ronald Reagan in 1968 has been subject to a recall effort, but Gray Davis was the first governor whose opponents gathered the necessary signatures to qualify for a special election.

Every artist she showed the script to had declined to take on the project, so it was offered to aspiring artist Arthur Adams, whose samples had been given to editor Carl Potts and Nocenti, his assistant editor, by editor Al Milgrom.

* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.

* Every constant function whose domain and codomain are the same is idempotent.

* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to