共查询到20条相似文献,搜索用时 15 毫秒
1.
Pierre Fraisse 《Journal of Combinatorial Theory, Series B》1985,39(2):146-152
We prove that any bridgeless graph G = (V, E), |E| = m, |V| = N, admits a cycle cover of total length at most . We give a quick survey of the related problems and establish some properties for the vertex covering problem and for shortest coverings of cographic matroids. 相似文献
2.
Michel Las Vergnas 《Discrete Mathematics》1978,23(3):241-255
We prove the following theorem: Let G be a graph with vertex-set V and ?, g be two integer-valued functions defined on V such that for all x ∈ V. Then G contains a factor F such that for all x ∈ V if and only if for every subset X of V, is at least equal to the number of connected components C of G[V ? X] such that either C = {x} and g(x) = 1, or |C| is odd ?3 and for all x ∈ C. Applications are given to certain combinatorial geometries associated with factors of graphs. 相似文献
3.
G = 〈V(G), E(G)〉 denotes a directed graph without loops and multiple arrows. (G) denotes the set of all Hamiltonian circuits of G. Put H(n, r) = max{|E(G)|, |V(G)| = n, 1 ≤ |(G)| ≤ r}. Theorem: . Further, H(n, 2),…, H(n, 5) are given. 相似文献
4.
A. V. Kostochka 《Journal of Graph Theory》1995,19(1):65-67
The following is proved: if every bridgeless graph G has a cycle cover of length at most 7/5|E(G)|, then every bridgeless graph G has a cycle cover of length at most 7/5|E(G)| such that any edge of G is covered once or twice. © 1995 John Wiley & Sons, Inc. 相似文献
5.
E.J Farrell 《Journal of Combinatorial Theory, Series B》1979,26(1):111-122
Let be a family of connected graphs. With each element α ∈ , we can associate a weight wα. Let G be a graph. An F-cover of G is a spanning subgraph of G in which every component belongs to . With every F-cover we can associate a monomial π(C) = Παwα, where the product is taken over all components of the cover. The F-polynomial of G is Σπ(C), where the sum is taken over all F-covers in G. We obtain general results for the complete graph and complete bipartite graphs, and we show that many of the well-known graph polynomials are special cases of more general F-polynomials. 相似文献
6.
We present an algorithm which finds a minimum vertex cover in a graph G(V, E) in time , where for connected graphs G the parameter a is defined as the minimum number of edges that must be added to a tree to produce G, and k is the maximum a over all biconnected components of the graph. The algorithm combines two main approaches for coping with NP-completeness, and thereby achieves better running time than algorithms using only one of these approaches. 相似文献
7.
D.R Woodall 《Journal of Combinatorial Theory, Series B》1978,25(2):184-186
A theorem is proved that is (in a sense) the best possible improvement on the following theme: If G is an undirected graph on n vertices in which for every non-empty subset S of the vertices of G, then G is Hamiltonian. 相似文献
8.
Yoko Usami 《Discrete Mathematics》1983,44(2):195-199
A simple graph with n vertices is called Pi-connected if any two distinct vertices are connected by an elementary path of length i. In this paper, lower bounds of the number of edges in graphs that are both P2- and Pi-connected are obtained. Namely if , then |E(G)|?((4i?5)/(2i?2))(n?1), and if , then |E(G)|?2(n?1) apart from one exeptional graph. Furthermore, extremal graphs are determined in the former. 相似文献
9.
A dominating cycle for a graph G = (V, E) is a subset C of V which has the following properties: (i) the subgraph of G induced by C has a Hamiltonian cycle, and (ii) every vertex of V is adjacent to some vertex of C. In this paper, we develop an O(n2) algorithm for finding a minimum cardinality dominating cycle in a permutation graph. We also show that a minimum cardinality dominating cycle in a permutation graph always has an even number of vertices unless it is isomorphic to C3. 相似文献
10.
Tatsuo Ohtsuki Lap Kit Cheung Toshio Fujisawa 《Journal of Mathematical Analysis and Applications》1976,54(3):622-633
This paper considers the problem of finding a minimal triangulation of an undirected graph G = (V, E), where a triangulation is a set T such that every cycle in G = (V, E ∪ T) has a chord. A triangulation T is minimal (minimum) if no triangulation F exists such that F is a proper subset of , and an ordering α is optimal (optimum) if a minimal (minimum) triangulation is generated by α. A minimum triangulation (optimum ordering) is necessarily minimal (optimal), but the converse is not necessarily true. A necessary and sufficient condition for a triangulation to be minimal is presented. This leads to an algorithm for finding an optimal ordering α which produces a minimal set of “fill-in” when the process is viewed as triangular factorization of a sparse matrix. 相似文献
11.
12.
D.R Woodall 《Journal of Combinatorial Theory, Series B》1973,15(3):225-255
The binding number of a graph G, bind(G), is defined; some examples of its calculation are given, and some upper bounds for it are proved. It is then proved that, if bind(G) ≥ c, then G contains at least disjoint edges if , at least disjoint edges if , a Hamiltonian circuit if , and a circuit of length at least if and G is not one of two specified exceptional graphs. Each of these results is best possible.The Anderson number of a graph is defined. The Anderson numbers of a few very simple graphs are determined; and some rather weak bounds are obtained, and some conjectures made, on the Anderson numbers of graphs in general. 相似文献
13.
《Applied Mathematics Letters》2002,15(5):623-626
For a graph G(V, E), if a proper k-edge coloring ƒ is satisfied with C(u) ≠ C(v) for uv ∈ E(G), where , then ƒ is called k-adjacent strong edge coloring of G, is abbreviated k-ASEC, and χ′as(G) = min{k | k-ASEC of G} is called the adjacent strong edge chromatic number of G. In this paper, we discuss some properties of χ′as(G), and obtain the χ′as(G) of some special graphs and present a conjecture: if G are graphs whose order of each component is at least six, then χ′as(G) ≤ Δ(G) + 2, where Δ(G) is the maximum degree of G. 相似文献
14.
Peter J. Slater 《Discrete Mathematics》1981,34(2):185-193
The concept of a k-sequential graph is presented as follows. A graph G with ∣V(G)∪ E(G)∣=t is called k-sequential if there is a bijection such that for each edgein E(G) one has. A graph that is 1-sequential is called simply sequential, and, in particular the author has conjectured that all trees are simply sequential. In this paper an introductory study of k-sequential graphs is made. Further, several variations on the problems of gracefully or sequentially numbering the elements of a graph are discussed. 相似文献
16.
Bondy conjectured [1] that: if G is a k-connected graph, where k ≥ 2, such that the degree-sum of any k + 1 independent vertices is at least m, then G contains a cycle of length at least: (n denotes the order of G). We prove here that this result is true. 相似文献
17.
Jun Fujisawa 《Discrete Mathematics》2008,308(12):2382-2388
Let G be a (k+m)-connected graph and F be a linear forest in G such that |E(F)|=m and F has at most k-2 components of order 1, where k?2 and m?0. In this paper, we prove that if every independent set S of G with |S|=k+1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min{d-m,|V(G)|} which contains all the vertices and edges of F. 相似文献
18.
19.
Laurence R Matthews 《Journal of Combinatorial Theory, Series B》1979,27(3):260-273
A matroidal family is defined to be a collection of graphs such that, for any given graph G, the subgraphs of G isomorphic to a graph in satisfy the matroid circuit-axioms. Here matroidal families closed under homeomorphism are considered. A theorem of Simöes-Pereira shows that when only finite connected graphs are allowed as members of , two matroids arise: the cycle matroid and bicircular matroid. Here this theorem is generalized in two directions: the graphs are allowed to be infinite, and they are allowed to be disconnected. In the first case four structures result and in the second case two infinite families of matroids are obtained. The main theorem concerns the structures resulting when both restrictions are relaxed simultaneously. 相似文献
20.
S.C Locke 《Journal of Combinatorial Theory, Series B》1982,32(2):206-222
Let G be a k-connected graph where k≥3. It is shown that if G contains a path L of length l then G also contains a cycle of length at least () l. This result is obtained from a constructive proof that G contains 3k2 ? 7k + 4 cycles which together cover every edge of L at least 2k2 ? 6k + 4 times. 相似文献