On （g, f）-Uniform Graphs

Gui-zhenLiu YanLiu
[1]DepartmentofMathematics,ShandongUniversity,Jinan250100,China [2]DepartmentofMathematics,SouthernNormalUniversity,Guangzhou510631,China

文章摘要:A graph G is called a (g, f)-uniform graph if for each edge of G, there is a (g, f)-factor containing it and another (g, f)-factor excluding it. In this paper a necessary and sufficient condition for a graph to be a(g, f)-uniform graph is given and some applications of this condition are discussed. In particular, some simple sufficient conditions for a graph to be an [a, b]-uniform graph are obtained for a ≤b.
文章主题:一致图 k-因子 简单离散 边集 子图生成

文章内容：,1.21,.1(2005)67—76('/)-,@-2005.,,,250100,(—:..)2,,510631,(,,)一,(,,)一(,,)一.(,,)一,[,61-.(,,)?;(,,)一;[,6】-;-200005701.()().,().6()()..9—()()()∈().(9,,)一()()()∈().()=()∈(),(,,)一,..,——..()一()=∈(),(口,.,)一『,—.(),—=『\1.()[].—.().(,)=(:∈,∈∈()(,)=【(,)1.一()(1=(1∈(1.(,)+∑().一()()1.,(),()()0.(,,,)(,,,)—()一()一(,,,)+()19701.1[.】-()()()∈().(,,)-0"15,200311,2004(10471078,10201019)(20040422004),,∑髭68()(,,,)0..正.正,(,,)一[].(,,)一[.[,]-[引.[1,11].(,,)一,(,,)一.(,,)一,(.,)一.(,,)一.(,,)一(,,)一,,(,,)一(,,)一(,,)一.,—[,6]_,.(,,)一(,,)一[,引.,[90]1-1-.1-1-.(,,)一1-.(,,)一..,[,]_.[,]_.—.2(9,/)-(夕,,)一.夕—()()()∈().,()=,1,￡2.1:1(,,夕,)=2.(1).(2)一()((),)1——一().1=1(1)(2)一()((),)21——一().】=0,._2=2(,,夕,)=2.(1).(2)一()((),)21——一().2=1(1)(2)一()((),)1～—一().2=0,.—),((),)1((),)1.=(,,夕,)=2—.(1).(2)≠一().￡=1(1)(2),≠0一().=0,.2.114[()(),?()∈().(,,)一,(,,)一,()=,(,,,)1692.2-0(1(),(),∈().日(,,)一,,',()=,6(,,,)￡2.(,,)?(,,).(,.厂)一,2.12.2::,5(,,,)=0.2,2.1..()(),(),∈().(,,)..()2--,—1.(),()=,5(,,,)-.(,)=(,,,,),5(,)=5(,,,)∈(),()=,().一(),2.1,.2.2?-().,一2?夕—,()=0.5(,)=—()一()一(,)+()(,)(,)=2,≠,"(,)=0,.1&;.[,61.2.1—(—1.().2.3(),:∈()\～())2.3[,6].,1≤&;.(),)(—)—()()=2;1()=1～((),)11()=0.2.4[7】<>0,10&;.妇力[,-,())(—)—2()2()=2;2()=1—((),1)1:2()=0.0<>∑=0<>∑=70...2.32.42.3.1&;.[,,/(),)(—)一￡(),(2.1)()一2;()=1≠()()=0.3【,6】-[,6_.[,叫一().∈().3.1.2.[,]一//,《1).(2).[,]一.[,]一(1)(2),[,6-[1,5】.2,[,6-.—,3.1.,==,—七一.≠,.3.2.,2&;.[+1,+1】-[,61..,.,.一0,1.1.2.3(2.1),,(),5())(—)一￡()()2.3.+1()+1∈(),∑(.+1一)(—)(+1)=0(1(+1))+—)(—)=(1(+1))(0+—)(—)=)(—)<>∑(,,)一和=(1/(6+1))∑(6+———++)(—)=珀1.1.1.1,2∈1∈1,…()71(3.2)::()\—(),1,.一,,1≠21(—)12(—)1..,1(—)2.=2(—+1)/(+1)2—2/(+1)()2/(+1)&;1,(3.1),1.2.1.()】1—2,=0+1一)(—)(+1)一2(1/(+1))∑(+—)=1=(1/(+1))(—)+2/(+1)—)(—)+2/(+1)一():(1/(+1))∑[(6一)+(—+1)](—)+26/(6+)7=1—()1()入(6一+—+1)/(+1)+2/(+1):(+2—+1)(+1)=1+(2—)/(+1)1一(2—)/(+1).(2—)/(+1)&;0,()一2(3.3)(3.4)&;一—.+—+—<>∑+仇/—.,1+—+—<>∑1+/1=一&;72—()=0∈,=[(6一)/(+1)]0(—)+2/(+1)=(—)(+1)+2/(+1).(+1)/(—),5()一1—2/(+1)...._..5()一2.(3.5)1&;(+1)/(—),()+1,+1()=(—)=1&;(+)/(—)(+1)(+1)/(—)+1.一2,..,5()一2.(3.6)2.≠().2=()\()2≠.,(,)1(,)1.(,)1∈—()1.=(1(+1))[(6一)+(—+1)](—)=0≥(—+1)/(+1)&;0.(,)1,5()一1∑(+1一)(—)(+1)一1=2=(1/(+1))(+—)(—)+/(+1)一5()一02(1(+1))[(6一)+(—+1)](—)+/(+1)/(+1)=5()—/(+1)..5()一1.(3.2)一(3.8),(2.1).(3.7)(3.8)(,,)一3.1.3.2:+1+1,,.3.1.1&;(1)=,1=,1=,2,…,0),1=,2,…,)(1)::1,16)'2.,1[,+1]一.10[,]_=2.,,1一,()∈.(,1).()∈1.(1,1)一2,.3.2.1—+12(2)=22,272=2=,2,…,"0+1),=,2,…,+(2)=:1+1,1+1)2).2[/+1,+2]一?3.12[.讣—2.『]后,..[(—1)/+1,『(△一1)]+1]一5=5()△=△().3.2.3.3..2(『(△一1)/1,[(5—1)/,『(△一1)/]一.5=△,(—1)=『(△[,6-.1)/』&;3.4.()+2,0&;