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Canonical Triangulation of a Graph, with a Coding Application

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(1)Canonical Triangulation of a Graph, with a Coding Application Luca Castelli Aleardi, Olivier Devillers. To cite this version: Luca Castelli Aleardi, Olivier Devillers. Canonical Triangulation of a Graph, with a Coding Application. RR-5231, INRIA. 2004, pp.24. �inria-00070765�. HAL Id: inria-00070765 https://hal.inria.fr/inria-00070765 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Canonical Triangulation of a Graph, with a Coding Application Luca Castelli Aleardi — Olivier Devillers. N° 5231 8 Juin 2004. ISSN 0249-6399. ISRN INRIA/RR--5231--FR+ENG. Thème SYM. apport de recherche.

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(211) ¯ T9z<¬PYfFY Y-£bdp~z<¬PY-pr`dY-}£zPW}£µ¥¶ il`wprY-}nmWyYQ} brgebdTnYhlzP`cbUbdpriˆzPnŒPhˆYP¦ §²bprY X*zPijW`xbrg£Y Wy ga}aY7bdTnY¸šAzPyY¸}nY ŒPprY Y*`dY-k5mnY-WyY>¼!zt|n|nhˆ_DijWŒ‰ztzP}nzP|abdiˆ¬PY¸zPpdijbdTnX7Y bdily*yga}aY p 5' ƒt‹ )2"xbdg‰y gPX7|nprY-`r`xbdTnY`dY-k5mnY-WyY ¶ žŸ.Y¸y zPz>y~TniˆY ¬PY*z>`c_DX7|abdgPbdily zPhjhˆ_£bdTWY*bdTnY-gPprYbriˆy-zthKfFgPmn9} Œ>ij¬>Y  f5_bdTnYY-5bdprgP|D_*gtš ¶ ApdY šMY pUbrg7bdTnY/nY 5bw`dY-ybdiˆgP šMgPpCzPY-5bdprgP|D_¸ztWzPhj_a`diˆ

(212) ` "'¦ — iˆWzthˆhj_Ÿ

(213) Y.gPnhˆ_TWz<¬>Y›brg™Y-Wyga}aY

(214) bdTnY2y gPnnYQy'brij¬Dijbu_!gtšWµ ¶ ¼NbdTnil`|nTWz>`cYU}agDY-`ngPb}nY |FY W}gPegPmnp zPhjŒ>gPpri brTnXzt9}ey-ztef9YCy-ztprpdiˆY-}gPmab›y~TWg5g5`ciˆnŒxgPnYUgPš9brTnY2­Dng”Ÿ2Y-Wyga}aiˆnŒ`cbdp~z”bdY-ŒP_šMg>pbdpriˆzPnŒPmWhˆzPp X7YQ`cTnYQ!` ('Ѓt#Š )²ž 'ˆ# +,)²ž 'ˆ )²ž 'j/ D#)2"x¦ §²šŸ

(215) YxmW`dYwbrTnY™prY-y Y 5bUgP|abrijX*zth»zPhjŒ>gPpri brTnXšMg>pU|nhˆzPWztp

(216) bdprilztnŒ>mnhˆztbdiˆgPW`

(217) fD_¸ogPmnhlzthˆTngP ztW}Zay~TWz”¢ LY JFY-B p 'ˆ, D#)²žtbrTnY2bdgPbrzPhWyg5`ub›}agDYQ`qngtb›}nY |FY W}7g>brTnYCŸUz<_!Ÿ.Y2gPfab~ztiˆnY-}eµ¥¶$ztW}eijb›iˆ`›zP`d_5X7|abrgtbriˆy-zthˆhj_ +± * ,-$/.60  fnijbr`-žnŸ2TnY prY  il`UbdTWY5mWXfFY p2gtš¬PY-pcbriˆy Y-`Ugtšq¯ ?ztW}gP𐵥¶brgDg "'¦.

(218)   G. . . . T 7U>595Œ % T. SUTWY/}nY-yga}aiˆnŒ*zthˆŒPg>pdijbdTWX¡`ub~ztpdbUŸ2ijbdTbrTnY!yga}aY/prY |nprY-`dY 5bdiˆnŒ7z7y ztWgPnily zPh9brpdilztWŒPmnhlz”brijg>µ¥¶Užnzt9} brTnYy gD}nY¸ygPprprY-`d|9g>W}aiˆnŒbdg+bdTWY`cYQk5mnY Wy Y U¶U¦  b!«Wp~`ub!Ÿ.Y¸}aY-y ga}aY¸iˆ$hˆiˆnY-zPpbdiˆX7Y¸µ¥¶ÀŸ2ijbdT½z }nY-yga}aY-p¥šMg>p¥bdprilztnŒ>hjYqX7Y-`dT¥žtzPW}xbdTnY.`cYQk5mnY Wy Y U¶U¦SUTnY !ijb`dm ¸yYQ`¥brgwzt|W|nhj_xgPmWp}aY bdpriˆzPnŒPmnhlz”brijg> zPhjŒ>gPpri brTnX bdg*g>fabrzPij bdTWYgPprijŒ>ijWzPhªŒPp~zt|nT+¯e¦  " 2! . .     . 453. . . =3 B;7 ;>\ ? > ; =6 ;T @'e!T = ?!7:@U9e. — iˆWzthˆhˆ_½Ÿ

(219) YŒPiˆ¬PY+ztmn|n|FY p*fFgPmWW}½brg$bdTnY£ztX7g>mn5begPš™fnijbr`7nYQyYQ`d`rztpr_$bdgpdYQyg>W`ubrpdm9y'b*z¤Œ>przP|nT ¯ `cbrztpdbdiˆnŒ$šMprgPX ijbr`¸y-ztng>nily zthUbrpdilztWŒPmnhlz”brijg>·µ¥¶U¦ÀZDiˆWyY£g>nhˆ_½bdTWY‰`cYQk>mWY Wy YgPš™šAz>yY£}aY-ŒPprY Y-` Mbdp~z<¬PY-pr`dY-}eiˆzŒPiˆ¬PY-*gPp~}aY p "il`›WY Y-}nY-}¸}amWpdiˆnŒbrTnY™}aY bdpriˆzPnŒPmWhˆztbdiˆgP*|nTWz>`cY>ž>Ÿ.YCŸ.gPmnhl}7iˆ>brY prY-`cbdYQ} iˆ+Y ¬”zthˆmWztbdiˆnŒbrTnYY 5brpdg>|5_gtšNbrTnil`C`cYQk5mnY Wy YP¦ âMãà¥âäß.

(220) <‚.  

(221)     . — gPpqbrTniˆ`›Ÿ

(222) YwpdY šMY pqbrg/bdTnY2brTnY g>pdY bdily zPhWztWzPhj_a`diˆ`|Wpdg”¬Dil}aY-}efD_ 'ˆ -„)9yg>WyY-pdniˆnŒ/brTnY2bdgPbrzPhnY 5bdprgP|D_ gPš»bdTnY™¬”zthˆY Wy Y#V”}nY ŒPprY YC`dY-k5mnY-WyYQ`Kiˆz ,”¢ÜX*zPni šMg>hˆ}7|FgPhˆ_DŒPg>*XeYQ`cTgtš¥ŒPY-DmW`›ÄW¦KÙmWp›prY-`dmnh bUy zP¸f9Y Y a|npdYQ`d`dY-}ijbrTnY/šMgPhˆhjg”Ÿ2iˆnŒeŸ.z<_ª¼  G  OÆD Ê G ’ Æ w l:  %T G& G  µ ¶ E³  G

(223) L G ZI

(224) ' O G  O      80 A : µ  ¶ ± 5:G

(225) Z

(226)  G   G G 

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(228) ` "'žWbdTnY-¤¯ 9 il`wz*`dijX7|n hˆY! Œ> przP |nTnYP¦ SUTWiˆ`UiˆX7|nhj_bdTWztbCŸ

(229) Yy-zt+ygPX7|nmnbdY!z7y zPngPnily zPhFbdpriˆzPnŒPmnhlz”brijg> gPš:¯ 9™brgDgW¦ ®NYb m9`yg>W`diˆ}aY-p &zt9} 9 žwpdYQ`c|FY-ybdiˆ¬PY hˆ_½brTnY‰buŸ.g·`dY-k5mnY-WyY‰gPš/šAzPyY©}aY Œ>pdY-Y-`zPW} ¬PY-pcbrY ¬”zPhjY-WyYQ`2zP`r`cgayilz”brY-}¸bdgebdTnY!y-ztng>nily zthªbrpdilztWŒPmnhlz”brijg>W`.µ ¶ žWµ ¶  ¦ <™`ciˆnŒzPztprijbdTnX7YbriˆywY Wy ga}aY p

(230) bdgeygPX7|nprY-`r`K`dY |WzPprztbdY-hj_ ztW } 9 Ÿ.Y™y-ztz>y~TnijY-¬PYwz>`c_DX7|abrgtbc¢ ily zPhjhˆ_*brTnY/bdTnY-gPprYbriˆy-zth»mn|n|FY p2fFgPmWW}ŒPiˆ¬PY fD_¸brTnYY 5bdprgP|D_*gPšbrTnY¬”zthˆY Wy #Y V”}nY ŒPprY Yx`cYQk5mnY Wy Y-`-¦q§²š Ÿ.Y!}aY-ngtbrY!fD_ I ztW}  L bdTnY!prY hlz”brij¬>Y/šMpdYQk5mnY Wy ijYQ`2gtšq¬>Y pdbdY ¬<zPhjY-WyY 

(231) zt9}šAzPyY}aY Œ>pdY- Y *iˆ£bdTnY buŸ.g*`cYQk5mnY Wy Y-` ÀztW} 9 žnbdTnY-ijpCY-5bdprgP|D_¸ztprY/pdYQ`c|FY-ybdiˆ¬PY hˆ_*Y a|nprY-`r`dY-}¸fD_ª¼. (

(232) %  L  0 ' f V<(š )‰ztW} 9 (% I  0 ' f V”¬ ) yL I I & L'& ´$Y y-zt½ng”Ÿ iˆX*ztŒPiˆnY*brg©zP|n|nhˆ_©g>mnp!brpdilztnŒ>mnhlz”bdiˆnŒ¤zPhjŒ>gPpri brTnX bdg‰fFgtbrT ¯zt9}½¯ 9 žqzPW}bdg m9`cY$gPnY$X7gPprY¤fnijb+bdg y~Tng>`dY¤fFYbuŸ.Y Y-Àµ¥¶¡zPW} µ¥¶ ”ž/}aY |FY 9}aijWŒ g> bdTWYy ga}aY$`di  Y-`gPš e, 9 ?yg>pdprY-`d|9g>W}aiˆnŒ7zP`d_5X7|abrgtbriˆy-zthˆhj_7brg  zPW}   9 "¦ §²š  ˆ  9 Ÿ.Y2yg>Xe|WmabdYUµ¥¶  zPW}Ÿ.YUpdY bdmnpr 9 žPŸ2ijbdT7Ä/zP`Y Dbrprz™fnij.b 5gtbdTWY prŸ2iˆ`dY

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