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1.
In this paper, we prove the following result:
Let G be a connected graph of order n, and minimum degree . Let a and b two integers such that 2a <= b. Suppose and .
Then G has a connected [a,b]-factor.
Received February 10, 1998/Revised July 31, 2000 相似文献
2.
Let G be a multigraph, g and f be integer-valued functions defined on V(G). Then a graph G is called a (g, f)-graph if g(x)≤deg
G(x)≤f(x) for each x∈V(G), and a (g, f)-factor is a spanning (g, f)-subgraph. If the edges of graph G can be decomposed into (g, f)-factors, then we say that G is (g, f)-factorable. In this paper, we obtained some sufficient conditions for a graph to be (g, f)-factorable. One of them is the following: Let m be a positive integer, l be an integer with l=m (mod 4) and 0≤l≤3. If G is an -graph, then G is (g, f)-factorable. Our results imply several previous (g, f)-factorization results.
Revised: June 11, 1998 相似文献
3.
图的(g,f)-因子和因子分解 总被引:10,自引:0,他引:10
设G是一个图,g,f是定义在图G的顶点集上的两个整数值函数且图G的一个(g,f)-因子是G的一个支撑子图F使对任意的x∈V(F)有本文给出了一个图(g,f)-可因子化的若干充分条件和一个图是(g,f)-消去图的充分必要条件,并研究了这些条件的应用。 相似文献
4.
图的(g,f)-因子和因子分解 总被引:17,自引:0,他引:17
设G是一个图,g,f是定义在图G的顶点集上的两个整数值函数且图G的一个(g,f)-因子是G的一个支撑子图F使对任意的x∈V(F)有本文给出了一个图(g,f)-可因子化的若干充分条件和一个图是(g,f)-消去图的充分必要条件,并研究了这些条件的应用。 相似文献
5.
设G是一个图,用V(G)和E(G)表示它的顶点集和边集,并设g和f是定义在V(G)上的两个整数值函数且g<f.图G的一个(g,f)-因子是G的一个支撑子图F使对任意的x∈V(G)有g(x)≤dF(x)≤f(x).如果过图G的任意k条边都有一个(g,f)-因子,则称图G是一个(g,f)-k-覆盖图.如果图G的任意k条边不属于它的一个(g,f)-因子,则称图G是一个(g,f)-k-消去图.作者分别给出了一个图是(g,f)-k-覆盖图和(g,f)-k-消去图的充分条件. 相似文献
6.
本文讨论一般含1-因子连通图的n次幂中边不交1-因子的个数.从而证明了L.Nebesky(1984)猜想对含1-因子图成立. 相似文献
7.
A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤s. We prove that an s-degenerate graph G has a total coloring with Δ+1 colors if the maximum degree Δ of G is sufficiently large, say Δ≥4s+3. Our proof yields an efficient algorithm to find such a total coloring. We also give a lineartime algorithm to find a total
coloring of a graph G with the minimum number of colors if G is a partial k-tree, that is, the tree-width of G is bounded by a fixed integer k. 相似文献
8.
《Quaestiones Mathematicae》2013,36(6):841-848
AbstractA set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected. We study the graphs for which adding any edge does not change the connected domination number. 相似文献
9.
Ciping Chen 《Graphs and Combinatorics》1994,10(2-4):97-100
A sharp bound of the toughness of a graph for the existence of a [2,b]-factor is given in this paper, whereb > 2. 相似文献
10.
11.
12.
There exists a constant C such that for every d-degenerate graphs G
1 and G
2 on n vertices, Ramsey number R(G
1,G
2) is at most Cn, where is the minimum of the maximum degrees of G
1 and G
2.* The work of this author was supported by the grants 99-01-00581 and 00-01-00916 of the Russian Foundation for Fundamental Research and the Dutch-Russian Grant NWO-047-008-006. The work of this author was supported by the NSF grant DMS-9704114. 相似文献
13.
On the 2-rainbow domination in graphs 总被引:2,自引:0,他引:2
The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G□K2. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is shown that for the generalized Petersen graphs GP(n,k) this number is between ⌈4n/5⌉ and n with both bounds being sharp. 相似文献
14.
A sufficient condition for graphs with circular flow index less than 4 is found in this paper. In particular, we give a simple
proof of a result obtained by Galluccio and Goddyn (Combinatorica, 2002), and obtain a larger family of such graphs.
* Partially supported by the National Security Agency under Grants MDA904-01-1-0022. 相似文献
15.
On(g,f)—Uniform Graphs 总被引:9,自引:0,他引:9
Thegraphsconsideredinthispaperwillbesimpleundirectedgraphs.LetGbeagraphwithvertexsetV(G)andedgesetE(G).ForavertexxofG,thedegreeofxinGisdenotedbydG(x).Theminimumdegreeandthemaximumdegree0fGaredenotedbyS(G)andb(G),respectively.Letgandfbetw0integer-valuedfunctionsdefined0nV(G)suchthatg(x)5f(x)foreveryx6V(G).Thena(g,f)-factorofGisaspanningsubgraphFofGsatisfyingg(x)SdF(x)5f(x)forallxEV(G).Ifg(x)=f(x)foreachxEV(G),thena(g,f)-factoriscalledanf-factor.Iffisaconstantfunctiontakingthevaluek,… 相似文献
16.
On (g, f)-Uniform Graphs 总被引:3,自引:0,他引:3
Gui-zhenLiu YanLiu 《应用数学学报(英文版)》2005,21(1):67-76
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. 相似文献
17.
18.
(mg+m—1,mf—m+1)—图的(g,f)—因子 总被引:8,自引:0,他引:8
本文证明了(mg+m-1,mf-m+1)-图具有一些特殊的(g,f)-因子,从而推广到了关于(g,f)-覆盖图和(g,f)-消去图的有关结果,有助于进一步研究(mg+m-1,mf-m+1)-图的正交因子分解问题。 相似文献
19.
不含有图K1,R的图称为K1,r-free图,设G是一个具有顶点集V(G)的图,设n(≥3),a和b是整数,使得b≥a≥1,若b是奇数,设b≥n-1。我们证明了每个连通的K1,r-free图G在b|V(G)|为偶数,它的最小度至少是a n-1,|V(G)≥ (2(a b)-1)(a b-1)/b,以及|NG(x)∪NG(y)|≥a|V(G)|a b对V的任意两个不邻接的点x和y都成立时,G有一个[a,b]因子。 相似文献