Cycles, minors and trees
119
0
0
Volltext
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(19) IoV _ L?n ¼ g L?VeJ ]TW V W VR|c JdHeIoV I?p!I`S )r 0 VeI W R H f L ^ `yH"LL _ L?n ýg L?V"J ]TW V Y] J ]TW P+L?n|z G=>=CJMP5C43ÛOG@<?A?U;JMU]G@<?ID ) t 0 :=<`×A ) r 0 U;YZ±`8]¶JMP`:XJ:DM2?R`DLCJ G=|{¼ÒU;D-G=±zC3<U;< ¼ÒU;| :=<?AG@<?8]¶ZU;|§U]J*UÔDG=±TC3<U;<»m¼ *5èC DMP?:=8;8z2?DLC(JMP?U;D|:=OJq|4MCC38]¶ZJMP?4MG@25>@P5G@25J*JMP5C O9P?:X±`JLC43 FP5C|£G@8;8;Gè{U;<?>8]C3YZYZ:¬qè{tP?UÔO9P DM2`YZr YZ:X49U]1C3DvDLG@YBC±`4MG=±TC4MJMU]C3DBG=| :X49OD:=<?AÝOU;49O8]C3D U;<WJLG=±TG@8]G=>@U]C3D DM:XJMU;DL|¶¬U;<5>) 0(:=<?A:) 0Q§O:=<êRTC±`4MG\=C3AêRK¶C38]C3YBC3<yJM:X4M¶¢)JMP?G@25>@Pã<5G=J OG@YB±`8;CJLC38]¶¸JL4QU]\KUÔ:=>8 0JLG=±zG@8;G=>@U;O:=8§:X4M>@2?YZC3<SJMD ,*¤KâcâÎ . - Ñ ACE ¼ F CqCV=[^Lp CP[op5XjEQb¢HoEyLa`hLJcLZ\^R;fnH EjX>f>kRX>Vi\×u;HV=[:M lÃm bhCV Cnu Cn]R H]rN 4 XQV ¼ p¸b$LvfCKCnV=[a`LX>V=EQfH]ZCIu Cn]nEjXjNCf<L]gCV=[vfy2 H V=[oCnuC]aR NX>]rNJwC ø XQV ¼XQV 2¸X>VNyJÙ]ZtC[if&`CfUCZNOCEjX>uu CCn]aJÙRIR3CZL[V \$CUL_!k 2¼ EQbhL_Ck2V p¸biXjNy]ZbgCf&Xj`E¸CZNaNOLEjV(X>u EyCnHJÙXQR Vf8HKV,NPXQL VYV(VEyCnH]WXQV`hfÈLXQ`=V(]ZE CZl6NX>< fk CJSR3X{fÈEjpWH/LuCPC[]\iE&CPCn¬ f 47 ø 4 ø L_k ¼ H E l FPK2?D7UÔ<B±`:X4MJMU;O2`8;:X43=C\=C4M¶ZOU]4QO8]C{U;< ¼Õ×´P?:=DØS:å2?<?U;ÀK25C,DLCJ7G=|$C3A?>=C3Dy:=<?AvèC(YZ:3¶ A5C·`<?C¸: NR^NJwC JLGWRTC¸JMP5C¸DM2?R?>=49:X±`PG=|H¼¿OG@<`DMU;DLJMU;<?>G=|{:=8;8C3A5>=C3D0OG@<SJM:=U;<?C3AcUÔ<: t3r.
(20) >@U]\=C3<¥OU]49O8]CåU;< ¼Ò)°:=<?AJMP?C\=C4MJMU;OC3DHU;<?OUÔA5C3<SJ{è{U]JMPwJMP5C3DMCC3A5>=C3Da0Q Ó G=JLCµJMP?:XJ{JMP?C3DLC U;<?O8Ô2?A5CZJMP5Cw2?D92?:=8·&<?U]JLC»O¶KO8]C3DBUÔ<²¼µ*:=<?A²U;<±`:X4MJMU;O2?8Ô:X4µU]JMDµ|°2?<?A?:=YZC3<SJM:=8qO¶¬O8]C3D )è{U]JMP»49C3DL±TC3OJFJLGv:=<y¶>@U;\=C3<DL±`:=<?<`U;<5>µJL4MCC0Q u <5G=JMP5C4BOG@<?A?U;JMU]G@<G@<cJMP5CJLG=±TG@8]G=>=¶G@< ¼ÙJMP?:XJ0DLCC3YZD0<?:XJM2549:=8*U;<c:WOG@<yJLCü¬J è{P5C49CBJMP5CvOU]49O8;C3D G=|,:w>=49:X±`P:X49CZJLGRTCB4MC±?49C3DLC3<SJLC3ARy¶êDM25R`>=49:X±`P?D OG@<?D9U;DLJMU;<5>wG=| JMP5C3U]4C3A5>=C3D U;DJMP?:XJC\=C4M¶åOU]4QO8]CU;D2?<?UÔÀy25C38;¶HA5CJLC4QYZU;<5C3ARy¶U;JMD¢C3A5>=C3D3@:=D JMP5C*O8;G@DM254MC G=| JMP5C3U]4F2?<`U]G@<$Û6ÀK2?U]\X:=8]C3<yJM8]=¶ 7 La`DI?p!I`S gyW ` g P1I ø Ï ¼ cJdHeI Y I?J øE# ¼ WZYD_ IoV Y I W V ø z )^³ 0 u 8]JMP5G@25>@Pè*C D9P?:=8;8z<5G=Jq|£G=49Yv:=8;8]¶B4MC3ÀK2?U]4MeC )^³ 0Q5JMP5C JLG=±TG@8]G=>@U]C3D*è*C-DMP?:=8;8zOG@<?DMU;A?C4|G=4 ¼t è(U;8;8KJM2549r <BG@2?J7JLGDM:XJMU;DM|£t ¶µº JMP?U;D7OG@<`A?U]JMU]G@<$=JLGKG57_(Gè*C\=C43 )^³ 0ÛA5GKC3D7<5G=J7|G@8;8]Gè |4MG@Y ) 0Û:=<`q A ) r 0a77U;<< 4KC3OJMU]G@< èCFD9P?:=8;85OG@<?DLJL4Q2?OJ: >=49:X±&PBè{U]JMPB: JLG=±TG@8]G=>=¶BDM:XJMU;DM|£¶¬U;<5> ) t 0q:=<?¢ u A|°:=YZ) U;0q8]¶JMP?) :X¼§J{&O0³1G@?<yvJM:=G=U;|F<?D{DM25:ZR?>=OU]4Q49:XO±`8]C-P?D OG@G=<`|{DM:U;DLJM>=U;<?49:X>µ±`C3P²<yJM¼¿U]4MC3è(8;¶vU;8;8 G=| RTC3Cv<?OA?:=D8; 8]C3A CZ[O\iCn_EQbXQV U]|,<5G C3A5>=C0G=|q¼Á8;U;C3D(U;<㧼 |£G=4 U;<5·&<?U]JLC38]¶wYZ:=<yq¶ M§:=<?A¥JMP5C fath} 1T §¼ G=|7JMP`U;DH|:=YZUÔ8]¶ U;D*JMP5C DM25R`>=49:X±`P¸G=|Û¼ OG@<?D9U;DLJMU;<5>µG=|:=8Ô8&C3A?>=C3DqJMP?:XJF8;U]CHU;<§¼ |G=4,:=<»GKA`A<K2?YåRTC4*G=| U;<?A`U;¯ OC3D §)°:=<?AwJMP?C-\=C4MJMU;OC3D(U;<?OU;A5C3<yJqè{U]JMP»JMP5C3DMC-C3A5>=C3aD 0Q :=DLC3AG@<JMP?CvOG@<?OC±?JµG=|,:O¶¬O8]C¸:=<?AG@254åA?C·`<?U]JMU]G@<êG=| ×´D92?YwØ]èCYZ:3¶<5Gè A5C·`<?C*JMP?C NR^NJwCÊf&`hH^NC «) ¼80G=|z: 8]G¬O:=8;8]¶-·`<`U]JLC>=4Q:X±`PZ¼:=DÛJMP5C,DLCJÛG=|zDM2?YZD G=|&C3A5>=C Ú JMP?U;<¸|°:=YZU;8;U]C3DG=|O¶¬O8]C3D |¼ U;D*·`<`U]JLC=yJMP?C3<»JMP?U;D*A5C·`<?U]JMU;G@<¸U;D*OG@YB±`:XJMU;R`8]CHè{U]JMPJMP5C DLJM:=<?A`:X49AG@<5oC )Cü5OC±?JåJMP`:XJåè*C¸<5Gè OG@<`DMU;A5C4µDM25R?>=49:X±&P?D-G=|(¼¿49:XJMP5C4µJMP?:=<C3A5>=C DLCJMaD 0Q _(Gè*C\=C43U;<ôG=49A?C4wJLGÝA5C·`<5CêJMP5CO¶¬O8]CDL±&:=OCã|£G=4>=4Q:X±`P?D»è{P?UÔO9PYZ:3¶ûP?:\=C U;<5·&<?U]JLC,A5C>=4MCC3D¬è*C(DMP`:=8;8?:=8;DLGåP?:3\=CHJLGåJM:XI=C :=OOG@2?<yJG=|§Yµ2?8]JMU;±`8;U;OU]JMU;C3DG=|$\=C49JMU;OC3DU;| è*Cèq:=<SJ :XJ8]C3:=DMJDL« G@YBC*DL±`:=<?<`U;<5>,JL4MCC3DJLG(Cü5U;DLJ¢è{P5G@DLC|2?<`A?:=YBC3<yJM:=8@O¶KO8;C3D¢>=C3<5C4Q:XJLC JMP5C O¶¬O8]C DL±`:=OC= <?A5CC3A$¬8]CJ{¼ RTC(JMP?CH>=4Q:X±`P»G=R?JM:=. U;<5C3A|4MG@Y J è*GZA?U;DLJMUÔ<?OJ\=C4MJMUÔOC3D :=<?; A mRy¶¥:=A?A?C U;<5>»® <5Cèù\=C4MJMU;OC38D + r+Ú :=<`A G@U;<?UÔ<5>vJMP5C3YJLGwRTG=JMiP W:=<`A å FP5C3<JMP5C±`:XJMP 7 i+ xU;Dµ:WèC38;8 A5C·`<5C3ADM2?Y G=|F·`<?U]JLCO¶KO8;C3Dµ:=OOG=4QA?U;<5>¥JLG JMP5C:XRTG\=CWA5C·`<?U]JMU;G@< )°:=<`AéP5C3<?OC:=<éC38]C3YZC3<SJZG=|HJMP5CO¶¬O8]CDL±`:=C OC 0QqR`2?JµJMP?C4MCU;D <5GDM±`:=<?<?U;<?>wJL4MCCZÿ G=|(¼Òè{P?G@DLCv|°2?<?A?:=YZC3<SJM:=87O¶¬O8]C3DµDM2?YäJLG 70:=<S¶D92?O9PDM2?Y è*G@2?8;AêOG@<?DMU;DMJHG=|qU;<5·&<?U]JLC38]¶wYZ:=<y¶|°2?<?A?:=YZC3<SJM:=8ÛO¶¬O8]C3D C3:=O9POG@<SJM:=UÔ<?U;<5> :=<?;A å :=<?A¥DLG»JMP5CµJ è*GC3A?>=C3D(G=|JMP5C0±`:XJMP Sÿ è*G@2?8;AW8;U]CåUÔ<WU;<?·`<?U]JLC38]¶»YZ:=<y¶DM2?YvYZ:=<?A?D )°OG@<yJL49:=A?U;OJMU]G@< 0Q _(C3<?OCqJMP5C4MCqU;D<5G DL±`:=<?<?UÔ<5>FJL4MCCqG=|T¼Ý|G=4 è{P?U;OQPJMP5C*|°2?<?A?:=YBC3<yJM:=8 O¶¬O8]C3DF>=C3<5C4Q:XJLCU]JMDFO¶¬O8]CDL±&:=OC= G-G\=C4QOG@YBC{JMP?UÔD ±?4MG=R`8]C3Yùè*CFDMP?:X49±zC3<0JMP?C,4MC3Ày2`U]4MC3YBC3<yJMD G@<BJMP5C{D92?YZDÛYZ:XI¬U;<5> 25EQb±wXQV JMP5C-O¶¬O8]C-DL±&:=OC=`:=D,|G@8;8]Gè(Dpq:=8;8$:0|°:=YZU;8]¶ ) §¼ &0³QT G=|ÛDM25R?>=49:X±&P?D*G=|:0>=49:X±&PW¼ U]|<5G\=C4MJLCüãG=Ú |F¼Ò8;U]C3D-U;<¼ fa|thG=}4U;<? ·`<?U]JLC38]¶Yv:=<S;¶ M 4¬GU;<ê±`:X4MJMU;O2`8;:X43$C\=C4M¶ JMP?U;<v|:=YvU;8]¶BU;DC3A5>=C JMP?U;<$5 û¢CJJMP5C ¼ G=|§:JMP`U;<Z|°:=YZU;8]¶0RTC{JMP?CHDM2?R?>=49:X±`P § G=|*¼ OG@<?D9U;DLJMU;<5>¸G=|:=8;8C3A5>=C3D JMP?:XJ 8;U]CµU;<êȼ 1? |G=4 :=<¥G¬A?NR^A¥NJw<yC22?fyYå`RTH^NaCC 4{ G=|*U;<?A?U;OC32D 8)°:=<?A JMP5CF\=C49JMU;OC3DU;<`OU;A5C3<yJÛè{U]JMP0JMP5C3DLC(C3A5>=C3aD 0QK:=«<?Av8]CJÛJMP?C )8 ¼ 0ÛG=|§¼!RTC,JMP5C DLCJ7G=|$:=8;8`DM2?YZDÛG=|TJMP?UÔ<0|:=YZUÔ8;U]C3D G=|$O¶KO8;C3D |§¼ûUÔD78]G¬O:=8;8]¶µ·`<?U]JLC=@JMP?C3<Bt JMº P5CFC3A5>=C Ú JMP`U;< |°:=YZU;8;U]C3DG=|TO¶KO8;C3D:X4MC,±?49C3OU;DLC38]¶åJMP5C,JMP?U;<0|°:=YZU;8;U;C3¤D )°D9U;<?OCqRy/¶ û§C3YvYZ: C\=C4M¶BO¶¬O8]C OG@<yJM:=U;<?U;<5>0:µ\=C4MJLCü vYå2`DLJ*:=8ÔDLGµOG@<yJM:=U;<wDLG@YZCHC3A?>=C-U;<?OU;A5C3<yJè(U]JMP 0Q?:=<?A»DLGµG@254 A5C·`<`U]JMU]G@<4MC3 A?2?OC3DFJLGZJMP?:XJF>@U]\=C3<C3:X498;U]C43 pq8;C3:X498]¶ ) 8¼ 0qUÔD,O8]G@DLC3A2?<`A5C4q·`<?U]JLC DM2?YvD5:=<?Aw:=DF:ZOG@<?DMC3Ày25C3<`OC-G=|G@2?4FYZ:=U;< 4MC3DM2`8]JM|D )°:=<?AWP5C3<?OCå:=D9DM2?YZU;<?>Z:vOG@<?O4MCJLCµJLG=±TG@8]G=>=¶w|G=4 8¼ 0,èCµDMP?:=8;8§DMCCå8;:XJLC4(JMP?:XJ t³.
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