共查询到20条相似文献,搜索用时 78 毫秒
1.
A well-known Theorem of Vizing states that one can colour the edges of a graph by Δ+ colours, such that edges of the same colour form a matching. Here, Δ denotes the maximum degree of a vertex, and the maximum multiplicity of an edge in the graph. An analogue of this Theorem for directed graphs was proved by Frank. It states that one can colour the arcs of a digraph by Δ+ colours, such that arcs of the same colour form a branching. For a digraph, Δ denotes the maximum indegree of a vertex, and the maximum multiplicity of an arc. We prove a common generalization of the above two theorems concerning the colouring of mixed graphs (these are graphs having both directed and undirected edges) in such a way that edges of the same colour form a matching forest. 相似文献
2.
Problems involving the dismantling of a digraph (graph) by removal of arcs (edges) are investigated. Some of these problems have good characterizations related to the familiar results about Euler trails, others are NP-complete. 相似文献
3.
We determine the maximum number of arcs in an Eulerian digraph of given order and diameter. Our bound generalises a classical result on the maximum number of edges of an undirected graph of given order and diameter by Ore (1968) and Homenko and Ostroverhii? (1970). We further determine the maximum size of a bipartite digraph of given order and radius. 相似文献
4.
斯琴巴特尔 《数学的实践与认识》2003,(2)
本文在我们以往研究基础上 ,得到了有向图 n· C 3优美的进一步性质 :两个无交有向图 n· C 3各自的公共顶点与一个新增加的顶点 ,分别用有向弧来连接 ,使该新增加顶点的出度为 2或入度为 2时 ,这样连接而得的有向图为优美图 相似文献
5.
G. Gutin 《Journal of Graph Theory》1995,19(4):481-505
A digraph obtained by replacing each edge of a complete m-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is calied a semicomplete m-partite digraph. We describe results (theorems and algorithms) on directed walks in semicomplete m-partite digraphs, including some recent results concerning tournaments. © 1995 John Wiley & Sons, Inc. 相似文献
6.
Alexandre Pinlou 《Discrete Mathematics》2006,306(24):3281-3289
A directed star forest is a forest all of whose components are stars with arcs emanating from the center to the leaves. The acircuitic directed star arboricity of an oriented graph G (that is a digraph with no opposite arcs) is the minimum number of arc-disjoint directed star forests whose union covers all arcs of G and such that the union of any two such forests is acircuitic. We show that every subcubic graph has acircuitic directed star arboricity at most four. 相似文献
7.
8.
Sufficient Conditions for Maximally Edge-connected and Super-edge-connected Digraphs Depending on the Size 下载免费PDF全文
Let D be a finite and simple digraph with vertex set V (D). The minimum degree δ of a digraph D is defined as the minimum value of its out-degrees and its in-degrees. If D is a digraph with minimum degree δ and edge-connectivity λ, then λ ≤ δ. A digraph is maximally edge-connected if λ=δ. A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree. In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough. 相似文献
9.
L. Babai 《Journal of Graph Theory》1985,9(3):363-370
We prove that every finite regular digraph has an arc-transitive covering digraph (whose arcs are equivalent under automorphisms) and every finite regular graph has a 2-arc-transitive covering graph. As a corollary, we sharpen C. D. Godsil's results on eigenvalues and minimum polynomials of vertex-transitive graphs and digraphs. Using Godsil's results, we prove, that given an integral matrix A there exists an arc-transitive digraph X such that the minimum polynomial of A divides that of X. It follows that there exist arc-transitive digraphs with nondiagonalizable adjacency matrices, answering a problem by P. J. Cameron. For symmetric matrices A, we construct a 2-arc-transitive graphs X. 相似文献
10.
Given a digraph (directed graph) with a labeling on its arcs, we study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NP-complete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that constructs this circuit. When this algorithm is applied to a de Bruijn graph, it obtains the de Bruijn sequences with lexicographically minimum label. 相似文献
11.
Consider a set of graphs and all the homomorphisms among them. Change each graph into a digraph by assigning directions to its edges. Some of the homomorphisms preserve the directions and so remain as homomorphisms of the set of digraphs; others do not. We study the relationship between the original set of graph-homomorphisms and the resulting set of digraph-homomorphisms and prove that they are in a certain sense independent. This independence result no longer holds if we start with a proper class of graphs, or if we require that only one direction be given to each edge (unless each homomorphism is invertible, in which case we again prove independence). We also specialize the results to the set consisting of one graph and prove the independence of monoids (groups) of a graph and the corresponding digraph.With 1 Firgure 相似文献
12.
We prove that every directed graph with n vertices at least 5n–8 arcs admits the complete symmetric digraph of order 4 as a minor. The result is sharp. This answers a question raised by Meyniel (1983). We conclude with some open problems. 相似文献
13.
Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with tree-and path-decomposition of graphs. In order to define decompositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider such a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrary fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it has access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition. 相似文献
14.
Nicola Apollonio 《Discrete Mathematics》2007,307(21):2598-2614
Can a directed graph be completed to a directed line graph? If possible, how many arcs must be added? In this paper we address the above questions characterizing partial directed line (PDL) graphs, i.e., partial subgraph of directed line graphs. We show that for such class of graphs a forbidden configuration criterion and a Krausz's like theorem are equivalent characterizations. Furthermore, the latter leads to a recognition algorithm that requires O(m) worst case time, where m is the number of arcs in the graph. Given a partial line digraph, our characterization allows us to find a minimum completion to a directed line graph within the same time bound.The class of PDL graphs properly contains the class of directed line graphs, characterized in [J. Blazewicz, A. Hertz, D. Kobler, D. de Werra, On some properties of DNA graphs, Discrete Appl. Math. 98(1-2) (1999) 1-19], hence our results generalize those already known for directed line graphs. In the undirected case, we show that finding a minimum line graph edge completion is NP-hard, while the problem of deciding whether or not an undirected graph is a partial graph of a simple line graph is trivial. 相似文献
15.
A colored mixed graph has vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (arc-color preserving) homomorphism from G to H. We study in this paper the colored mixed chromatic number of planar graphs, partial 2-trees and outerplanar graphs with given girth. 相似文献
16.
A digraph H is immersed in a digraph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. For graphs the same relation (using paths instead of directed paths) is a well-quasi-order; that is, in every infinite set of graphs some one of them is immersed in some other. The same is not true for digraphs in general; but we show it is true for tournaments (a tournament is a directed complete graph). 相似文献
17.
A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly
one common vertex or cross at exactly one point interior to both arcs. About 40 years ago, J. H. Conway conjectured that the
number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many
edges as vertices. Some related problems and generalizations are also considered.
Received July 11, 1995, and in revised form April 16, 1996. 相似文献
18.
卜月华 《数学的实践与认识》2009,39(4)
唯一泛圈有向图D是一个定向图,对每一个n,3≤n≤υ,D中有且只有一个长为n的有向圈.用g(υ)表示具有υ个顶点的唯一泛圈有向图最小可能的弧数,用N(υ)表示具有υ个顶点、g(υ)条弧且互不同构的唯一泛圈有向图的个数.确定了当υ=3,4,5,6,7,8时的N(υ). 相似文献
19.
The competition graph of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of G is the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of the important research problems in the study of competition graphs to characterize a graph by its competition number. Recently, the relationship between the competition number and the number of holes of a graph has been studied. A hole of a graph is a cycle of length at least 4 as an induced subgraph. In this paper, we conjecture that the dimension of the hole space of a graph is not smaller than the competition number of the graph. We verify this conjecture for various kinds of graphs and show that our conjectured inequality is indeed an equality for connected triangle-free graphs. 相似文献
20.
Yoshio Sano 《Graphs and Combinatorics》2013,29(5):1543-1547
The notion of a competition graph was introduced by Cohen in 1968. The competition graph C(D) of a digraph D is a (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. In 1978, Roberts defined the competition number k(G) of a graph G as the minimum number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of the important research problems in the study of competition graphs to characterize a graph by its competition number. In 1982, Opsut gave two lower bounds for the competition number of a graph. In this paper, we give a generalization of these two lower bounds for the competition number of a graph. 相似文献