- P(gun)]
2016Փ_}ô
2016Փ_}ô?СoҽBƪҿ֪
2016Փ_}ô(1)
һ.
O(sh)ӋӋW(xu)һTdľC߅W(xu)оαCO(sh)Ӌă(yu)ȺЧԼָ(do)O(sh)Ӌչ_O(sh)ӋҪƌW(xu)Ӌ@һѳɞF(xin)O(sh)Ӌ繲Rr҇I(y)(ni)O(sh)ӋӋW(xu)J(rn)Rcо߀]иO(sh)Ӌl(f)չҪIJᘌ҇O(sh)ӋF(xin)ԓW(xu)ƵĽ̌W(xu)һƌW(xu)֮ЧO(sh)ӋӋڞO(sh)ӋW(xu)O(sh)ӋõO(sh)ӋķṩҪָ(do)
.W(xu)g(sh)rֵ
1. x}(j)
ӋڽuɞһT@W(xu)(w)СճI(lng)x_ӋССijɹĿ̶ܴ϶XX،(do)ʩ(yng)ӋӡӋW(xu)d֪R(jng)rYԴϻĴڅӳˇg(sh)O(sh)ӋW(xu)I(lng)҂l(f)F(xin)ӋͬИOİl(f)չgO(sh)ӋαC(yu)O(sh)Ӌ@ҪƌW(xu){(dio)оҪ(zhn)ķλҪԔO(sh)Ӌ(j)ҪĽM@Щc҂ͨʽL(fng)x“O(sh)Ӌ”ஐɵĹO(sh)ӋӋă(ni)_MO(sh)ӋӋһՓĆ}ڌW(xu)gĽںϳɞ鮔(dng)ǰW(xu)g(sh)Ĵh(hun)O(sh)ӋӋ(yng)ԓԴͨO(sh)ӋI(y)gķhȡóɹO(sh)Ӌṩ֮Чķϵ֧
O(sh)ӋMңO(sh)ӋӋһ̶ȵоO(sh)Ӌоȡñ^ĽY(ji)F(xin)һЩЧķ缼g(sh)A(y)yƌW(xu)ȷϵy(tng)O(sh)Ӌ(chung)O(sh)Ӌ߉O(sh)Ӌ̖O(sh)ӋģMO(sh)ӋԪ(yu)O(sh)ӋɿO(sh)ӋӑB(ti)O(sh)ӋģO(sh)Ӌ@Щ(c)ڲͬČI(y)O(sh)ӋO(sh)ӋӋRͬO(sh)ӋI(y)ҪһNϵ`ĽQ}Ӌ@Ҫ҂ᘌӋČW(xu)cĬF(xin)еij͵ķȺM្Y(ji)һm(yng)F(xin)rO(sh)ӋӋ
2. (chung)Լy
Q߷cP(gun)O(sh)Ӌоijɹ, ԇDһ҇O(sh)Ӌf_еĿ猣I(y)O(sh)ӋӋķwϵ
ڏĺЧĽǶO(sh)ӋӋˆTṩڲٿأұںI(y)O(sh)ӋMМͨķҪԓHI(y)O(sh)ӋF꠵Ӌh(hun)(ji)ãwO(sh)ӋˆTĵO(sh)ӋҲ(yng)ָ(do)@Ҫᘌ҇O(sh)ӋF(xin)ć(ni)W(xu)I(lng)ĿP(gun)MоxƌW(xu)Cϵ̎(chung)һЧӋmȻP(gun)ɹI(y)ѳڱͬ(c)ؽǶȵķпY(ji)ӋҪ҂֪J(rn)Rͬr҂O(sh)ӋI(y)ĹҎ(gu)猣I(y)Ч
3. оĿԺͺ
ڇHO(sh)Ӌgľ҇O(sh)ӋrLJ(ni)O(sh)ӋϵijN]Ժ҇͜I(y)猦O(sh)ӋӋJ(rn)֪в߀ȱһڽ̌W(xu)͌`кڲO(sh)ӋӋ(jng){(dio)(dng)ǰW(xu)(ni)HеĎױP(gun)ҲHڌijЩO(sh)ӋcĺεĽB]к܌I(y)؏ӋČMϵy(tng)UЈBƪ۠P(gun)ҪǏЈIN̹O(sh)ӋTI(y)O(sh)ӋӋ߂F(xin)ָ(do)áؽ@ôһI(y)^O(sh)ӋӋՓF(xin)ijN̶ijF(xin)O(sh)ӋӋ@һTdW(xu)ƣǎW(xu)Õհļg(sh)ĽǶȶҲஔ(dng)?sh)ĿڷԺO(sh)Ӌ߄n̵Ľ̌W(xu)ў֮e˴rČ`(jng)YԺĽܘ(gu)@猣I(y)оĿ˳ֵYԴϵĜ(zhn)
4.A(y)ڳɹ
A(y)?jn)?sh)12f֞ՓcɴHUO(sh)ӋӋP(gun)(ni)ҪƳO(sh)ӋӋĸc漰ҪW(xu)QߌW(xu)J(rn)RՓՓ(chung)W(xu)W(xu)ОMW(xu)W(xu)W(xu)O(sh)ӋW(xu)ʷW(xu)TW(xu)I(lng)KһƌW(xu)ЧķӰHָ(do)һģн̌W(xu)ָ(do)õČI(y)F(xin)ڱѴYռA΄(w)Aµĕrg(ni)ҌYMзY(ji)ɷƹ
һ. ȫ(gu)
O(sh)Ӌ-O(sh)ӋӋW(xu)о
ǰ
һ. ˼SĊW
1. ̾ĽQ֮
2. ȫX\-X˼SĊW
3. ˼S
4. ճе˼S
.O(sh)Ӌ
1. ϵy(tng)O(sh)Ӌϵy(tng)-\O(sh)Ӌ
2. O(sh)Ӌ-O(sh)ӋӋW(xu)d
a. O(sh)ӋӋW(xu)Ҫ
b. O(sh)ӋӋW(xu)İl(f)չcǰ
c. O(sh)ӋӋW(xu)Ľɫ
3. O(sh)ӋӋՓ
4. Step to step-Ӌչ_(ȫ֮)
5. һ(w)
6. Ӌ
a. Ҫ
b. ʩҪ
c. ӋĘ(gu)
d. ӋıF(xin)
7. ʮ˰-Ӌ߽B
.Ӌ߅
a. ̎̎ĽԌW(xu)-ԸQҕӖ(xn)
b. ų_şoɵĶՓ
c. Ҫľ
d. B(yng)Ч\÷rg
ӛ
. Ŀ(Hжʮl)
1.mQ—CA(y)yc(jng)IQߡ/̵g? —ɶس200010
2.a/ [] ɭ? _?;wg? —Aij 20024
3. оĿԺͺ
ڇHO(sh)Ӌgľ҇O(sh)ӋrLJ(ni)O(sh)ӋϵijN]Ժ͜ԣ҇I(y)猦O(sh)ӋӋJ(rn)֪в߀ȱһڽ̌W(xu)͌`кڲO(sh)ӋӋ(jng){(dio)(dng)ǰW(xu)(ni)HеĎױP(gun)ҲHڌijЩO(sh)ӋcĺεĽB]к܌I(y)؏ӋČMϵy(tng)UЈBƪ۠P(gun)ҪǏЈIN̹O(sh)ӋTI(y)O(sh)ӋӋ߂F(xin)ָ(do)ؽ@ôһI(y)^O(sh)ӋӋՓF(xin)ijN̶ijF(xin)O(sh)ӋӋ@һTdW(xu)ǎW(xu)Õհļg(sh)ĽǶȶҲஔ(dng)?sh)ĿڷԺO(sh)Ӌ߄n̵Ľ̌W(xu)ў֮e˴rČ`ԣ(jng)YԺĽܘ(gu)@猣I(y)оĿ˳ֵYԴϵĜ(zhn)
4.A(y)ڳɹ
A(y)?jn)?sh)12f֣֞Փcɴ棬HUO(sh)ӋӋP(gun)(ni)ҪƳO(sh)ӋӋĸc漰ҪW(xu)QߌW(xu)J(rn)RՓՓ(chung)W(xu)W(xu)ОMW(xu)W(xu)W(xu)O(sh)ӋW(xu)ʷW(xu)TW(xu)I(lng)KһƌW(xu)ЧķӰHָ(do)һģн̌W(xu)ָ(do)õČI(y)F(xin)ڱѴYռA΄(w)Aµĕrg(ni)ҌYMзY(ji)ɷƹ
2016Փ_}ô(2)
1}x,
Ҫо(ni)ݼMQP(gun)IԆ}
2ՓҪо(ni):
ȺcayleyDhamiltonȦ·ĴԆ},ҪnjһЩͳõȺM˚w{cY(ji).
3}x:
1.߶ȳȺw,׃Ɍ(yng)ȺĽY(ji)(gu)ĿҊģ.2.ڃɂF(xin)ҪW(xu)"ȺՓ"c"DՓ"֮g(lin)ϵ.3.߀҂ȺһЩ""——ѭh(hun)Ⱥ,wȺ,Ⱥֱe,Ԫ\P(gun)ϵMһ˽c(f)(x).4.Ҫ,оԓ}XȤζM.
4QP(gun)IԆ}:
һЩȺĈDαʾhamiltonȦ·ĴԆ}M˚w{cY(ji),ԇĈDC҂ϤĶƳһЩY(ji).hamiltonȺhamilton·cayley({(a,0),(b,0),(e,1)}:q4+zm) hamiltonȦĴ,Dcayley({(a,0),(b,0),(e,1)}: q8+zm) hamiltonȦĴMC.Y(ji)һЃɂԪMɵğocayleyDP(gun)|(zh),eČs6cayleyDhamiltonȦĴMӑՓ.
5Փ(j)о(chung)֮̎
ڱMȺcayleyDĸһЩõȺMоw{.оȺcayleyDʹ҂ȺJ(rn)R,^һЩȺcayleyDă(yu)|(zh).оԓ}HԌѭh(hun)Ⱥ,wȺ,Ⱥֱe,Ԫ\P(gun)ϵMһ˽c(f)(x),XʮȤ.
о(chung)֮̎njȺһЩcayleyDʾ,ͨ^D^yȺcȺ֮gP(gun)ϵ(Ⱥֱe),һЩȺhamiltonȦ·ĴMCcƏV.hamiltonȺ,q4+zm, q8+zm,s6cayleyDhamiltonȦĴ.
6īIĿ
1YL,DՓcW(wng)j(lu),,Ї֘I(y),xx.7
2 i.grossman w.magnus, groups and their graphs
3 igor pak and rados radoicic, hamilton paths in cayley graphs
7wżwM
2³——2µώocҵIJMо
3³——3ѮP(gun)Y
3ѮՓķ,_ʼ.
4³ó,ώָ(do)Mĺͼm.
5ѮՓ.
Փ_}ôP(gun)£
ôI(y)Փ_}01-12
I(y)Փ_}Ҫô06-08
_}ô03-24
ʿ_}ô01-26
ӢZI(y)I(y)_}-_}ô12-30
_}ô06-08
_}īICô02-24
Փ_}06-17
Փĵ_}07-23
Փ_}12-20