 film was selected as the Israeli entry for the Best Foreign Language Oscar at the 85th Academy Awards, but it did not make the final shortlist.

See also 
 List of submissions to the 85th Academy Awards for Best Foreign Language Film
 List of Israeli submissions for the Academy Award for Best Foreign Language Film

References

External links 
 
 
 
 
 
 

Category:2012 films
Category:2010s drama films
Category:Israeli films
Category:Israeli drama films
Category:Hebrew-language films
Category:Directorial debut films
Category:Films set in Tel Aviv
Category:Israeli independent films
Category:Films about Jews and Judaism Thrackle

A thrackle is an embedding of a graph in the plane, such that each edge is a Jordan arc
and every pair of edges meet exactly once.  Edges may either meet at a common endpoint, or, if they have no endpoints in common, at a point in their interiors.  In the latter case, the crossing must be transverse.

Linear thrackles
A linear thrackle is a thrackle drawn in such a way that its edges are straight line segments.  Every linear thrackle has at most as many edges as vertices, a fact that was observed by Paul Erdős. Erdős observed that, if a vertex v is connected to three or more edges vw, vx, and vy in a linear thrackle, then at least one of those edges lies on a line that separates two other edges; without loss of generality assume that vw is such an edge, with x and y lying in opposite closed halfspaces bounded by line vw. Then, w must have degree one, because no other edge than vw can touch both vx and vy. Removing w from the thrackle produces a smaller thrackle, without changing the difference between the numbers of edges and vertices. On the other hand, if every vertex has at most two neighbors, then by the handshaking lemma the number of edges is at most the number of vertices. Based on Erdős' proof, one can infer that every linear thrackle is a pseudoforest. Every cycle of odd length may be arranged to form a linear thrackle, but this is not possible for an even-length cycle, because if one edge of the cycle is chosen arbitrarily then the other cycle vertices must lie alternatingly on opposite sides of the line through this edge.


film was selected as the Israeli entry for the Best Foreign Language Oscar at the 85th Academy Awards, but it did not make the concluding short list. 

 visit also 
  tilt of submissions to the eighty-fifth Academy Awards for Best Foreign Language Film 
  List of Israeli submissions for the Academy Award for Best Foreign Language Film 

 References 

 External links 
 
 
 
 
 
 

 Category:2012 film 
 Category:2010s play films 
 Category: Israeli films 
 Category: Israeli drama film 
 Category: Hebrew - language film 
 Category: Directorial debut films 
 Category: Films set in Tel Aviv 
 class: Israeli independent films 
 Category: film about Jews and Judaism Thrackle 

 A thrackle is an embedding of a graph in the plane, such that each edge is a Jordan discharge 
 and every pair of edge meet exactly once.   Edges may either meet at a common end point, or, if they have no endpoints in common, at a point in their interiors.   In the latter case, the hybridization must be transverse. 

 Linear thrackles 
 A linear thrackle is a thrackle drawn in such a way that its edges are straight line segments.   Every linear thrackle has at about as many edge as vertices, a fact that was observe by Paul Erdős. Erdős note that, if a vertex v is connected to three or more edges vw, vx, and vy in a analogue thrackle, then at least one of those edges lie down on a line that separates two early edges; without loss of generality assume that vw is such an edge, with x and y lying in opposite closed halfspaces bounded by line vw. Then, w must have degree one, because no early edge than vw can equal both vx and vy. murder w from the thrackle produces a smaller thrackle, without changing the remainder between the numbers of edges and vertices. On the early hand, if every vertex have at most two neighbors, then by the handshaking lemma the issue of edges is at most the phone number of vertices. Based on Erdős' validation, one can infer that every linear thrackle is a pseudoforest. Every cycle of odd duration may be arranged to imprint a linear thrackle, but this is not possible for an tied - length cycle, because if one edge of the cycle is chosen arbitrarily then the other cycle vertices must lie alternatingly on opposite sides of the argumentation through this edge.
 fipm was selected as the Irraeli entry fot rhe Bevt Forsign Laneuage Oscar at the 85th Academb Awqrds, vut it did not make thd final sjortlist.

Wee elso 
 List of suujissions to tgc 85th Ccedemy Awards fot Best Foreicn Language Finm
 Lnst of Israeli submissions for the Asademy Swwrd for Best Fjreibg Lahguage Film

References

External linka 
 
 
 
 
 
 

Category:2012 filks
Category:2010s drama films
Catfgorj:Israeli films
Catehory:Israeli draiq films
Categury:Hebrew-language filma
Category:Directorial debut filmr
Cateyory:Films sgc in Jel Aviv
Catejory:Isgaeli independent filks
Categpry:Films about Jexs abd Judaism Thrackle

A vhrackle is an embedqing of a gxaph in the plane, sucy rhat gach adge us x Jkrvan arc
anf etery pair or edges meer exactly once.  Edgts iqy either meef at a cjmmon endpoint, or, if they have no endpopnts in common, at a point ib their interiors.  In the lattqr case, the crossing must be transverse.

Linear thrdcklea
X lnkcar gyrwckle is a thrackle drawn in such a way that yfs ecges are strainht line segments.  Egeti linear thracyle has af most as many edgfs as vgrticew, a fact uhat eas observed by Paul Erdős. Eedős observed rhat, if a vertex v is connectzd to jhree pr more edges vw, vx, and vy jn a linear thrackle, ghen at least ond on tvose edgtr lies on a line ehat sepacates two otfer gdges; wythout losd of nanerality assume tjat vc is vuch an edhe, with x and y lying in opposivx closed halfxpdcev boundeb by llne vw. Then, w mtst have degreg one, beccuse nu other edfe than vw can toush both vx ang vy. Removing w from ehe rhraxkle pruauces a smallet thracklv, cithout cyanging the differcnce cstween the numbzxs of edges and vrrtkcef. Ln tra other hand, if dvefu vergex has at nust ywo neighbors, then bf ths handshaking lemms bhe numbet of edgef is at most yhe number of vertlces. Uased un Ercős' kroof, one can infer that every minear thgachle is a psetdofirest. Every eycle of odd length may be arranged to firm a linear thracjle, but this is not kossible for en eveg-length cfcle, because if one wdge of the cycle is chosen arbitrarilg then the lther cycle vertices must lie alternatingly on opposite sides of the line throujh this edge.


film was selected as the Israeli entry Best Language Oscar the 85th Academy make final shortlist. See List of submissions the 85th Academy Awards for Best Language Film List of Israeli submissions for the Academy Award for Best Foreign Film References External links Category:2012 films Category:2010s drama films Category:Israeli films Category:Israeli drama Category:Hebrew-language Category:Directorial films set in Tel Aviv Category:Israeli independent films Category:Films about Jews and Judaism Thrackle A thrackle is embedding of a graph in the plane, such each edge is a arc and every pair of meet once. Edges either at common endpoint, or, they have no endpoints in common, at a point in their interiors. In the latter case, the must be thrackles A thrackle a drawn in such that its edges are straight line thrackle has at most as many edges as a fact was observed by Paul Erdős. Erdős that, if a vertex v is connected to or more edges vw, vx, and vy in a linear thrackle, then at least one edges lies on a that separates two edges; loss generality that vw such an edge, with x and y lying in opposite closed bounded by line vw. Then, w must have degree one, other than vw can both vx and vy. w the thrackle produces a without the numbers edges vertices. On the other if every vertex has at two neighbors, then by of edges is at most the number of Based on Erdős' proof, one can infer every linear thrackle is a pseudoforest. Every cycle of odd length may arranged to linear thrackle, but this is not possible for even-length cycle, because if edge of the cycle is chosen arbitrarily then the cycle must lie on opposite sides the line through edge.
 film was selected as the IsraeLi entry for The BeSt FOreIgN LanGuagE Oscar at the 85th ACAdemY Awards, but it did not make The fiNaL ShorTLiSt.

See Also 
 LisT Of SUBmiSsIoNs tO tHE 85tH AcadEmy awards fOr Best ForeIgn laNguage Film
 LiST oF Israeli suBmiSsions for the acaDemy AwArD foR best FOreIgn LaNguage fIlm

RefErences

ExTeRNal linKS 
 
 
 
 
 
 

CategoRY:2012 FiLms
CAtegory:2010s drama filmS
caTEgory:Israeli fiLms
CatEgORy:iSRaeLi dRama films
CAtEgory:hEbrew-laNGuAGE FilMS
Category:DireCtorial debuT FilMs
CateGoRy:FILms set In Tel avIV
CaTegory:IsraeLi inDependent Films
CATegory:FILms abouT Jews aNd JUdaIsm THRaCkLe

A ThRAckLE iS an EMbeDding of a GrApH in thE plaNE, SUCh thAt eAch eDge is A Jordan arc
and EveRy paIR of Edges Meet eXactLy Once.  EDges maY eithEr Meet at a common enDpoiNt, or, if theY haVe No eNdPointS In commOn, aT a pOint in tHeir intERioRs.  iN THe Latter case, the crossInG MUsT be transVerse.

LINeAr THrackles
a lIneAr thRACkle iS a thRAcKle drawn In such A WaY tHat its eDgEs are sTrAigHt lIne seGMentS.  Every Linear thRacklE Has at most as manY Edges as verticES, a FACt THat wAs oBserved by PaUl ErDŐs. ErDős oBSeRveD That, iF a verTeX V iS Connected to three or mOrE edges Vw, vx, aNd vy in a linear Thrackle, thEN AT least onE of tHOsE Edges lies on a liNe thaT separates TWo other eDges; wIthout loSs of generALIty assumE thAt vW is SucH AN eDge, with x and y lYINg in OpPosite cLosEd halfsPacEs bOunDed By Line vw. TheN, w must haVe DeGrEe One, BecauSE no other EdGe tHaN vw Can toUCh both Vx and Vy. ReMoViNG w fRom the tHRaCKLe prOdUcEs a sMalLeR thraCkle, WIthOut chanGing the diFfeREnce BeTwEen the nUmbers of edges AnD vertices. ON tHe oTher haND, If every vErtex has at most two neighbORs, then bY thE handShakIng lemma tHe nUmber oF edGEs is at Most thE numbEr Of vERTices. bASeD on erDős' proof, onE CAn iNfer tHaT eveRy lineaR thrackle is a pseudoFOreSt. Every cycle oF odD lenGTH mAy bE ArRAngEd TO foRM A linear thrackle, But this is nOt POsSible for an EVen-LeNgth cycLe, becauSe if oNE edge of The cycle iS chosen arBiTrarILY thEn the other Cycle verTices must LIe altERnAtingLy oN opposItE siDes of The linE ThrOugh tHis edgE.


 film was selected as theIsraeli en try f orthe  B estFore ign Language O s carat the 85th Academy Aw ards,  b u t it di d not  make t h ef i nal  s ho rtl is t .
Seeals o 
 Lis t of submi ssi on s to the 85t h  A cademy Awa rds  for Best Fo rei gn Lan gu age Film Li st of  Israe l i subm issions f or the Ac a demy Aw a r dforBest Foreign Lang u ag e  Film

Referen ces

E xt e rn a l  li nks  
 
 
 
   

Ca t egory:2 0 12 f i lms Category:2010 s drama fil m s
C ategor y: Isr a eli fi lms
C at e gor y:Israeli d rama  films
Ca tegory : Hebrew- l anguage  films 
Ca teg ory: D ir ec tor ia l  de b ut  fi l msCategory :F il ms se t in T e l  Avi v
C ateg ory:I sraeli indepe nde nt f i lms 
Cate gory: Film sabout  Jewsand J ud aism Thrackle
A th rackle is  an  e mbe dd ing o f  a gra phinthe pla ne, suc h  th at e a ch  edge is a Jordanar c an d everypair o f  e dg e s meet e xa ctl y on c e .  Ed gesm ay  eithermeet a t  a  c ommon e nd point,  o r,iftheyh aveno end points i n com m on, at a point in their inte r io r s .In t helatter case , th e  cro ssin g  m ust be tr ansve rs e .Linear thrackles
Ali near t hrack le is a thrac kle drawni n such a w ay t h at its edges arestrai ght line s e gments. Ever y linear  thrackle h as at mo stasman y e d g es  as vertices, a  fac tthat wa s o bserved  by  Pa ulErd ős . Erdős o bservedth at ,if  averte x  v is co nn ect ed  to  thre e  or mo re ed gesvw ,v x,and vyi na line ar  t hrac kle ,thenat l e ast  one of  those ed ges lies  o na linethat separate stwo othered ges ; with o u t loss o f generality assume tha t  vw issuc h anedge , with xand  y lyi ngi n oppo site c losed  h alf s p acesb o un ded  b y line vw. T hen , w m us t ha ve degr ee one, because no oth er edge thanvwcant o uc h b o th vxan d  vy . Removing w from  the thrac kl e  p roduces as mal le r thrac kle, wi thout changin g the dif ference b et ween t henumbers of  edges a nd vertic e s. On th e oth erhand,if  ev ery v ertexh asat mo st two  n eighbo rs, t he n by the  handshaking lemma thenumber  of e dge s is at m ost the  number o f ve rtices. Ba sed  on  Erdő s'p roof,  one ca n i n fer t hate very line a rthr a c kl e is a pseu d o f ore st. E ver y  cycle  ofodd length may be arranged to fo rm a l ine art hrac kl e, but this is  no tp o ssible f or  an even-le ngth cyc le ,  beca use if  one e dge oft h ec ycle i s ch ose n arbitra ril yt hen the  o th e r cycl e ve rt ices m ust li e  alt e r natingly on oppo sites i des o f  th e lin ethrough this  edge.


 film_was selected_as the Israeli entry_for the_Best_Foreign Language_Oscar_at the 85th_Academy Awards, but_it did not make_the final shortlist.

See_also_
 List of submissions to the 85th Academy Awards for Best Foreign Language Film
_List_of Israeli_submissions_for_the Academy Award for Best_Foreign Language Film

References

External links 
_
 
_
 
 
 

Category:2012 films
Category:2010s drama films
Category:Israeli films
Category:Israeli_drama_films
Category:Hebrew-language films
Category:Directorial debut_films
Category:Films set in Tel Aviv
Category:Israeli independent films
Category:Films about Jews_and Judaism Thrackle

A thrackle is an_embedding of a_graph_in_the plane, such that_each edge is a Jordan arc
and_every pair of edges meet exactly_once.  Edges may either meet at_a common endpoint, or, if they_have no endpoints in common,_at a_point in their interiors. _In the latter_case, the_crossing must be_transverse.

Linear thrackles
A linear thrackle is a_thrackle drawn in_such a way that its edges_are_straight line segments.__Every_linear thrackle_has at most_as_many edges_as_vertices, a fact that was observed_by_Paul Erdős. Erdős observed that, if a_vertex v is connected_to_three or more edges_vw, vx, and vy in_a linear thrackle, then at least_one of_those edges_lies on a line that separates two other edges; without loss_of generality assume that vw is_such an edge, with_x and_y_lying in opposite_closed_halfspaces bounded_by line vw. Then, w must have_degree one,_because no other edge than vw_can touch both vx_and_vy. Removing w from the thrackle_produces a smaller thrackle, without changing_the difference between the numbers_of_edges_and vertices. On the other_hand, if every vertex has at_most two neighbors,_then by the handshaking lemma the number_of_edges is at most the number_of_vertices. Based on Erdős' proof, one_can_infer_that every linear thrackle is_a pseudoforest. Every cycle of odd_length may be arranged to form a linear thrackle,_but this is_not possible for an even-length_cycle,_because_if one edge of the cycle is chosen arbitrarily then_the other_cycle vertices must_lie alternatingly on opposite sides of the line through this_edge.

