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C " "] `}  d* 0 / B3 3fԔ8c?"x HH   L cN NN}/kGrjL#j_   0 C \ " @0  N cN NN}/kGroRjL#j_ B  s *޽h ? fff̙80___PPT10.(02 B 0 B(      0  WvWr(Graph Coloring) ޞWr(Vertex Coloring) \eWG N PWGvޞWr/fcN P1uV(G) fNvQxe [nvuuvpGvu-Nv0viQޞBf (u)`"(v)0vu|(V(G))|= kBf GRS1zp/fGvN P k-Wr0V*P^g(3c^g"    H  0޽h ? 3380___PPT10. h @ (   Z  0L@  [ 1.1ޞWrxe Chromatic Number N PWGvޞWrxe (G) = min{k |GSN(uk POrWX}Y}0 SN(u POrWX}Y _NSNXebG/fk-SWrk-colorable 0ZPP)c Vg H  0޽h ? 3380___PPT10. nkl~ P~(  F  0P  J}TL 1.2 N(G)NhG-Ng'Y[hQP[Wvޞxe GR(G)(G)0 }TL 1.3 (G)(G)+10 If: Ne0W(u{1,2,& ,(G)+1}-NvOrOWXޞ O_[nޞWrvW,ghN g_N[SN[bkNޞ giR NvOrSN(u 0  NIf-N@b(uvWrel N,_N1zp/fGreedy Coloring0P'cggcgcggfg   EH  0޽h ? 3380___PPT10. xnd    `d (    0a , |2}TL 1.4 vu b Bf (G)=(G)+10 }TL 1.5 N'v^xeRp000000 GR0000000000 0 If N000006q_1u0YWr e/fWX0viBf]}(uNvOrgYS g0000 Vdk(WOrk0000000Y1v`l NN[SN[bWr0FPLc!gc!gcgo.gd ;^  6((\  S A ?? ^  6\  S A ??j0  ^   6\   S A  ??m ){  ^   6\   S A  ??G C  ^  6\   S A  ??P nR   ^  6\  S A  ?? E   ^  6^  6\  S A ??   \  S A  ?? @  H  0޽h ? 3380___PPT10. @?!ov v(  t  0 g }TL 1.6 00N(G)NhG-N|_dk Nv0g'YޞƖTvޞxehszxe Independence Number GR00000000 If 00Wv TOrvޞb_bN PhszƖIndependent Set 0<P'c g g g g g c #g Z^  6\  S A  ??2/ I  H  0޽h ? 3380___PPT10. ܚo p(  `  0}Z [ 1.7K-LuW k-critical graphs 00/f(G) = k N \e@b g'vckproper P[W( (H) < k GR'1zp/fN Pk-LuW0 _t 1.8 /fGpN Pk-LuW GR(G) k-10 If:Yg(G) < k-1 Ndeg(v) =(G)0s(W HQ(uk-1 POrWX}YG-v QWXvsSS[b YdkNOGvWrxe N'Yek-1 GP-wv Vdk(G) k-10 P c:gcggcQggT       H  0޽h ? 3380___PPT10. L p (  (     0<7  [t 1.9 Szekeres-Wilf 1968 0000000000 If N(G)=k GR_[X[(WN PGvP[W G [/fN Pk-LuW 01u_t1.8 00000000000 0'B0(c g c g o #g      ^  6\   S A  ??m  ^  6\   S A  ??0   H  0޽h ? 3380___PPT10. s}pJ $J(  $ $ 0tw  [t 1.10 Nfp[e@b gW@bbƖTGvN P[ g0 P2Fc g g c g g g    H < 0޽h ? 3380___PPT10. s @(  @ @ 0L7  T[t 3.4 NGpwQ gpޞvW GR 1 0 2 0@/PPc$Ag$d^ @ 6\ @ S A 3??fcS  3^ @ 6\ @ S A 4??  9  4H @ 0޽h ? 3380___PPT10. +t h`0H(  H, H 0wj  J[ 4.8 [(G ; k)p1uV(G) f{1,2,& ,k}@b g N TvޞWrQxeKN Pxe0 @bNGpk-SWrKNEQhNp (G ; k) 10(G ; k)_N1zp/fGvk-WrY_k-Chromatic Polynomial 0 O m > n0.P2P 02ccGgRg ^ H 6\ H S A 5?? =  5^ H 6\ H S A 6?? q  6H H 0޽h ? 3380___PPT10. pu< @L<(  Lp L 0̋wg _t 4.9 NTpwQ gnޞv9jW GR 0 [t 4.10 N GR(G;k)=(G e;k)-(Ge;k) GeNhbG-Nve.~bNޞ0 PBc c g c c 5g ^ L 6\ L S A 7??t 2 7^ L 6\ L S A 8?? gj  8H L 0޽h ? 3380___PPT10. P~vu~ PP~(  PF P C A*01gy H P 0޽h ? 3380___PPT10. Pyu :2`T(  T T 0 /dw  2v[t 4.11 (G;k)pkv|V(G)|!kY_ [v\Oxep1 ,{Nؚ!kxevOxep-|E(G)|02<c$4g$f   H T 0޽h ? 3380___PPT10. @MHv pX(  X X 0\< I\ *WrEdge-Coloring [ 5.1ckWr WGvN Pckk-Wr/fN P1uE(G) f{1,2,& ,k}vQxe [nvu N TviQ Bf(e)`"(f) PBfPG_N1zp/fN Pk-SWrk-edge-colorable 0O_GpSWr@bvg\OrxeN,N'(G)h:y  PxeChromatic Index N,1zp/fG vWrxe0V!P2g$cg   ^ X 611\ X S A 9?? p  9H X 0޽h ? 3380___PPT10. v  ($(  (r ( S )-A`}   r ( S h'. `  H ( 0޽h ? fff̙@ d@(  d d 0D  }TL 5.7 NPp|__hW GR'(P)=40 }TL 5.8 NPpwQ gGYxeޞvckGRW GR'(G)>(G)0P2&c$c$g$c$c$g$l   H d 0޽h ? 3380___PPT10. "x  ,$(  ,r , S -A`}   r , S .    H , 0޽h ? fff̙ XPh(  h h 0 01  [ 5.9N͑W Overfull N PWG/fn GRG1zpN͑W0 }TL 5.10 NGpN PN͑W GR'(G) > (G)0 }TL 5.11 N͑Wvޞxe_pGYxe0P%P2 P2cc!gccgcc g  ^ h 6\ h S A <??/m y <H h 0޽h ? 3380___PPT10. ْx   l (  l l 0 'Z |[t 5.12 YgG/fk-Sfr GR_X[(WN Pk-Wr O_ \eNav 0 If YgX[(W gi,j [PQsvxev] N\e2 NiQ PƖTR%Rp S N 0s(W N @b\QvP[Wp 0(W -NSvRWpvPW vPxev_NSGYxev_1ue k 'Y @bNGYxev__6qX[(W N_v>\iQGWWX NOri0s(W S(W_ NbijiQ POrNc sSS.~\  v]ݍ0 c T#jvek_|~~ NSsSS_I0 =P(cc=ggg . s &^ l 6\ l S A  =??3:z  =^ l 6\ l S A! >?? p, >^  l 6\  l S A" ???Y ?^  l 6%%\  l S A# @??  @^ l 6\  l S A$ A?? %  A^ l 6\ l S A% B??t  B^ l 6\ l S A& C??S 6  C^ l 6\ l S A& D??T 6  D^ l 6\ l S A' E??c q m s  E^ l 6\ l S A' F??   F^ l 6\ l S A( G??c P W s  G^ l 6\ l S A( H??   HH l 0޽h ? 3380___PPT10. `JyF pF(  p p 0/  [t 5.13Vizing[t NGpN,WSimple Graph 0GR'(G) (G)+10 [ 5.14Class 1 and Class 2 Wrxep(G)vWG1zp/f,{N^WClass 1 N/f(G)vWp,{N^W0*P2Nc c g  g c c -g    H p 0޽h ? 3380___PPT10. 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