共查询到20条相似文献,搜索用时 62 毫秒
1.
WANG Weifan 《系统科学与复杂性》2000,(2)
1. IntroductionLet G be a graph with vertex set V(G), edge set E(G), maximum degree A(G), minimumdegree 8(G), vertex chromatic number X(G), and edge chromatic number X'(G). G is equitablyk-colorable if V(G) can be pajrtitioned icao k independent sets VI, V2,'', Vk such that llKI III 1 5 1 for all i and j. The such smallest integer k as above is called the equitable chromaticnumber of G, denoted by X= (G). Similaxly we can define the equitable edge chromatic numberof a graph G and d… 相似文献
2.
Let G be a 2-edge-connected simple graph.We give a sufficient condition in which for anyx,y∈V(G),there is an(x,y)-trail which contains every vertex of G(x-y is allowed)exceptsome graphs. 相似文献
3.
YANJin LIUGuizhen 《系统科学与复杂性》2004,17(4):532-537
H. Wang considered the minimum degrees condition that G has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let m > 3, n > 2 and k >1 be three integers. Let G = (V1,V2;E) be a bipartite graph with | V1| = | V2| =n > 2k 1. If the minimum degreefor any cycle C of G with length 2m, then G contains k vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp. 相似文献
4.
BIPANCYCLISM IN HAMILTONIAN BIPARTITE GRAPHS 总被引:1,自引:1,他引:0
It is shown that if G is a hamiltonian bipartite graph on 2n vertices and δ(G)>2n/5 2,where n≥60,then G is bipancyclic. 相似文献
5.
MINIMUM FILL-IN PROBLEM OF GRAPHS 总被引:1,自引:0,他引:1
YUAN Jinjiang 《系统科学与复杂性》1996,(3)
MINIMUMFILL-INPROBLEMOFGRAPHSYUANJinjiang(DepartmentofMathematics,ZhengzhouUniversity,Zhengzhou450052,China)ZHANGHeping(Depar... 相似文献
6.
LONG DOMINATING CYCLES IN GRAPHS 总被引:1,自引:0,他引:1
SUN Zhiren 《系统科学与复杂性》1998,(4)
1.IntroductionAllgraphsconsideredinthispaperwillbefiniteandsimple.WeuseBondyandMurty[1]forterminologyandnotationsnotdefinedhere.LetG=(V,E)beagraphofordernandCbeacycleinG.Ciscalledadominatingcycle,orbrieflyaD--cycle,ifV(G)\V(C)isanindependentsetinG.ForavertexvinG,theneighborhoodofvisdenotedbyN(v),andthedegreeofvisdenotedbyd(v).FortwosubsetsSandTofV(G),wesetNT(S)~{vET\S:N(v)nS/0}.WewriteN(u,v)insteadofNV(G)({u,v})foranyu,vEV(G).IfFandHaretwosubgraphsofG,wealsowriteNF(H)insteado… 相似文献
7.
LIUYan WANGShiying 《系统科学与复杂性》2004,17(1):33-38
The maximum matching graph of a graph has a vertex for each maximummatching and an edge for each pair of maximum matchings which differ by exactly oneedge. In this paper, we prove that the connectivity of maximum matching graph of abipartite graph is equal to its minimum degree. 相似文献
8.
A NOTE ON COMPLETELY POSITIVE GRAPHS 总被引:1,自引:0,他引:1
XU Changqing 《系统科学与复杂性》2000,(2)
1. IlltroductionPioneered by M. Hall Jr. in 195811] and investigated by A. Berman [2--4] and J. H. Drew, C.R. Johnson and Loewy[5] et al., completely positive matrices have been shown their importancenot only in the study of block designs in combinatorial analysis[6], but also in establishingeconomic model.[7].Recall that an n x n matrix A is said to be completely positive, denoted by A E CPu, ifthere edest m nonnegative column vectors hi,'', ba such thatwhere I denotes transpose. The … 相似文献
9.
In the paper the homomorphisms of generalized de Bruijn-Good graphs aredescribed in detail and all homomorphisms of de Bruijn-Good graphs are giveu as anexample. 相似文献
10.
11.
DU Shaofei 《系统科学与复杂性》1996,(1)
VERTEX-PRIMITIVE1/2-TRANSITIVEGRAPHS¥DUShaofei(DeportmentofMathematics,ShanxiUniversity,Taiyuan030006,China)Abstract:Inthispa... 相似文献
12.
SHI Ronghua 《系统科学与复杂性》1997,(1)
1.IntroductionThefollowingNash--william'stheoremtellsusthatthehamiltonianproblemconcerningbipartitegraphsisimportant,thoughwedonotseemuchliteratureonit.Theorem111]Thejollowingproblemsareequivalent:1)thedete~inationofallhamiltoniangmphs,2)thedete~inationof… 相似文献
13.
THE LINEAR ARBORICITY OF COMPOSITION GRAPHS 总被引:1,自引:0,他引:1
WU Jianliang 《系统科学与复杂性》2002,(4)
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G) 1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs. 相似文献
14.
GAO Jingzhen 《系统科学与复杂性》1996,(1)
PANCONNECTIVITYAND2-CONNECTEDCLAW-FREEGRAPHS¥GAOJingzhen(DepartmentofMathematics,ShaddockNormalUniversity,Jinan250014,China)Z... 相似文献
15.
LI Xiangwen 《系统科学与复杂性》1998,(4)
1.IntroductionWeconsideronlysimplefinitegraphs.OurbasicnotationandterminologynotdefinedherefollowthOSeofBondyandMurtyll].ForagraphG,letV(G)andE(G)(orjustVandE)deDOtelievertexsetandedgeset,respectively.Wedenoteapathandacyclecontaining8veniCesbyPaandCarespectively.ThecycleCaiscalledans-cycle.Denotebyg(G)(orbrieflybyg)thegirthofG1.SetNC=min{IN(u)UN(v)l:tv相似文献
16.
XU Baogang 《系统科学与复杂性》2002,(3)
Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2 circuits. In this paper, we propose a new conjecture which is equivalent to Hajos' conjecture, and show that to prove Hajos' conjecture, it is sufficient to prove this new conjecture for 3-connected graphs. Furthermore, a special 3-cut is considered also. 相似文献
17.
HUANG Qiongxiang LIU Xin Department of Mathematics Xinjiang Univerasity Urumchi China 《系统科学与复杂性》1993,(3)
In this paper we obtain the necessary and sufficient condition for the connec-tivity of the Cayley color graphs or the Cayley graphs to be equal to their minimum degree.The sharp lower bounds of connectivity of Cayley color graphs and the Cayley graphs arealso obtained. Our results generalize the previous results obtained in [1] to [3]. 相似文献
18.
GAO Taiping 《系统科学与复杂性》1997,(2)
1.IntroductionWeuse[1]forterminologyandnotationsnotdefinedhereandconsidersimplegraphsonly.FOragraphG,wedenotebyV(G)thevertexsetofG,byE(G)theedgesetofG.ForanyxEV(G),AgV(G),BgV(G)--AandanysubgraphSofG,weputDenotebyG[A]thesubgraphofGinducedbyA.LetCbeacycleof… 相似文献
19.
LIU Yiping WU Zhengsheng Department of Mathematics Nanjing Normal University Nanjing China 《系统科学与复杂性》1993,(4)
In the paper, the (k-1)-traceable-nice ((k-1)-T-nice) and k-homogeneously-traceable-nice (k-HT-nice) sequence are defined similarly to the definition of k-Hamilton-nice (k-H-nice) and (k+1)-Hamilton-connected-nice ((k+1)-HC-nice) sequence. Therelationships among these four nice sequences are discussed. The main results are asfollows: Let_η=(a_1, a_2,…, a_(k+1) be a non-negative rational sequence, k≥2. (1) If η is(k+1)-HC-nice and a_(k+1)=2, then η is k-HT-nice, (2) If η is k-HT-nice and a_(k+1)=2,then η is (k-1)-T-nice, (3) If η is k-H-nice, then η is k-HT-nice. Meanwhile, four unsolvedproblems on these topics are proposed. 相似文献
20.
In[1],P.Paulraja posed the following problem:Let G be a 2-connected graph suchthat δ(G)≥3,where δ(G)denotes the minimum degree of G.If each edge of G lies on either a cycle oflength 3 or a cycle of length 4,is it true that G has a spanning Eulerian subgraph?A related case inwhich δ(G)≥4 is settled affairmatively in this paper. 相似文献