共查询到20条相似文献,搜索用时 15 毫秒
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A. Abouelaoualim K. Ch. Das W. Fernandez de la Vega M. Karpinski Y. Manoussakis C. A. Martinhon R. Saad 《Journal of Graph Theory》2010,64(1):63-86
Sufficient degree conditions for the existence of properly edge‐colored cycles and paths in edge‐colored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edge‐colored multigraph of order n on at least three colors and with minimum colored degree greater than or equal to ?(n+1)/2? has properly edge‐colored cycles of all possible lengths, including hamiltonian cycles. Longest properly edge‐colored paths and hamiltonian paths between given vertices are considered as well. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 63–86, 2010 相似文献
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D. De Werra 《Discrete Mathematics》1976,14(2):133-138
Usual edge colorings have been generalized in various ways; we will consider here essentially good edge colorings as well as equitable edge colorings. It is known that bipartite multigraphs present the property of having an equitable k-coloring for each k ? 2. This implies that they also have a good k-coloring for each k ? 2. In this paper, we characterize a class of multigraphs which may be considered as a generalization of bipartite multigraphs, in the sense that for each k ? 2 they have a good k-coloring. A more restrictive class is derived where all multigraphs have an equitable k-coloring for each k ? 2. 相似文献
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D. De Werra 《Journal of Graph Theory》1981,5(3):247-258
Some classes of graphs are described which are extensions of bipartite multigraphs. Exclusion of some specific partial subgraphs gives some properties of edge colorability. in particular sufficient conditions are developed for the existence of generalized good and equitable colorings. 相似文献
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David Cariolaro 《Journal of Graph Theory》2006,51(4):301-318
We introduce a unifying framework for studying edge‐coloring problems on multigraphs. This is defined in terms of a rooted directed multigraph , which is naturally associated to the set of fans based at a given vertex u in a multigraph G. We call the “Fan Digraph.” We show that fans in G based at u are in one‐to‐one correspondence with directed trails in starting at the root of . We state and prove a central theorem about the fan digraph, which embodies many edge‐coloring results and expresses them at a higher level of abstraction. Using this result, we derive short proofs of classical theorems. We conclude with a new, generalized version of Vizing's Adjacency Lemma for multigraphs, which is stronger than all those known to the author. © 2005 Wiley Periodicals, Inc. J Graph Theory 51: 301–318, 2006 相似文献
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D. de Werra 《Discrete Mathematics》1979,27(3):309-316
A general framework for coloring problems is described; the concept of regular coloring is introduced; it simply means that one specifies in each edge the maximum and the minimum number of nodes which may have the same color.For several types of regular colorings, one defines canonical colorings where colors form an ordered set and where one always tries to use first the “smallest” colors. It is shown that for some classes of multigraphs including bipartite multigraphs, regular edge colorings corresponding to maximal color feasible sequences are canonical. 相似文献
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Takao Nishizeki 《Discrete Mathematics》1981,37(1):105-114
The lower bounds on the cardinality of the maximum matchings of regular multigraphs are established in terms of the number of vertices, the degree of vertices and the edge-connectivity of a multigraph. The bounds are attained by infinitely many multigraphs, so are best possible. 相似文献
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We consider multigraphs G for which equality holds in Vizing's classical edge colouring bound χ′(G)≤Δ + µ, where Δ denotes the maximum degree and µ denotes the maximum edge multiplicity of G. We show that if µ is bounded below by a logarithmic function of Δ, then G attains Vizing's bound if and only if there exists an odd subset S?V(G) with |S|≥3, such that |E[S]|>((|S| ? 1)/2)(Δ + µ ? 1). The famous Goldberg–Seymour conjecture states that this should hold for all µ≥2. We also prove a similar result concerning the edge colouring bound χ′(G)≤Δ + ?µ/?g/2??, due to Steffen (here g denotes the girth of the underlying graph). Finally we give a general approximation towards the Goldberg‐Seymour conjecture in terms of Δ and µ. © 2011 Wiley Periodicals, Inc. J Graph Theory 69:160‐168, 2012 相似文献
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An edge‐coloring of a graph G with colors is called an interval t‐coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In 1991, Erd?s constructed a bipartite graph with 27 vertices and maximum degree 13 that has no interval coloring. Erd?s's counterexample is the smallest (in a sense of maximum degree) known bipartite graph that is not interval colorable. On the other hand, in 1992, Hansen showed that all bipartite graphs with maximum degree at most 3 have an interval coloring. In this article, we give some methods for constructing of interval non‐edge‐colorable bipartite graphs. In particular, by these methods, we construct three bipartite graphs that have no interval coloring, contain 20, 19, 21 vertices and have maximum degree 11, 12, 13, respectively. This partially answers a question that arose in [T.R. Jensen, B. Toft, Graph coloring problems, Wiley Interscience Series in Discrete Mathematics and Optimization, 1995, p. 204]. We also consider similar problems for bipartite multigraphs. 相似文献
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Flavia Bonomo Guillermo Durán Martín D. Safe Annegret K. Wagler 《Discrete Applied Mathematics》2013,161(13-14):1925-1942
A graph is balanced if its clique-matrix contains no edge–vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work, we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to graphs that belong to one of the following graph classes: complements of bipartite graphs, line graphs of multigraphs, and complements of line graphs of multigraphs. These characterizations lead to linear-time recognition algorithms for balanced graphs within the same three graph classes. 相似文献
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Michael S. Cavers Randall J. Elzinga Sarah E. Vanderlinde 《Discrete Mathematics》2008,308(15):3230-3240
We consider the minimum number of cliques needed to partition the edge set of D(G), the distance multigraph of a simple graph G. Equivalently, we seek to minimize the number of elements needed to label the vertices of a simple graph G by sets so that the distance between two vertices equals the cardinality of the intersection of their labels. We use a fractional analogue of this parameter to find lower bounds for the distance multigraphs of various classes of graphs. Some of the bounds are shown to be exact. 相似文献
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H. IshiiT. Matsutomi 《Mathematical and Computer Modelling》1995,22(10-12)
We consider a P model version of stochastic spanning tree problems with random edge costs. Parameters of underling probability distribution of edge costs are unknown and so they are estimated by a confidence region from statistical data. The problem is first transformed into a deterministic equivalent problem with a minimax type objective function and a confidence region of means and variances, since we assume normal distributions with respect to random edge costs. Our model reflects the situation that the maximum possible damage due to an unknown parameter should be minimized. We show the problem can be reduced to the deterministic equivalent problem of another stochastic spanning tree problem, which is already investigated by us. Thus, we can find an optimal spanning tree of the original problem very efficiently by this reduction. 相似文献
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Stefan Grünewald 《Journal of Graph Theory》2000,33(4):240-245
A multigraph M with maximum degree Δ(M) is called critical, if the chromatic index χ′(M) > Δ(M) and χ′(M − e) = χ′(M) − 1 for each edge e of M. The weak critical graph conjecture [1, 7] claims that there exists a constant c > 0 such that every critical multigraph M with at most c · Δ(M) vertices has odd order. We disprove this conjecture by constructing critical multigraphs of order 20 with maximum degree k for all k ≥ 5. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 240–245, 2000 相似文献
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对图G的一个k-正常变染色法f,若图G中任意相邻两点的相邻边色集合互相不包含,那么称f为图G的一个k-Smarandachely邻点边染色(简记为k-SEC),而最小的正整数k称为图G的Smarandachely邻点边色数.尝试应用Lovasz局部引理来得到了Smarandachely邻点边色数的上界. 相似文献
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Balázs Ráth 《Random Structures and Algorithms》2012,41(3):365-390
We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting models where the sequence of initial multigraphs is convergent in a sense which is a natural generalization of the notion of convergence of dense graph sequences, defined by Lovász and Szegedy (J. Combin. Theory Ser B 96 (2006) 933–957). We investigate how the limit object evolves under the edge reconnecting dynamics if we rescale time properly: we give the complete characterization of the time evolution of the limit object from its initial state up to the stationary state, which is described in the companion paper (Ráth and Szakács, in press). In our proofs we use the theory of exchangeable arrays, queuing and diffusion processes. The number of parallel edges and the degrees evolve on different timescales and because of this the model exhibits subaging. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 相似文献
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1977年, Myerson建立了以图作为合作结构的可转移效用博弈模型(也称图博弈), 并提出了一个分配规则, 也即"Myerson 值", 它推广了著名的Shapley值. 该模型假定每个连通集合(通过边直接或间接内部相连的参与者集合)才能形成可行的合作联盟而取得相应的收益, 而不考虑连通集合的具体结构. 引入图的局部边密度来度量每个连通集合中各成员之间联系的紧密程度, 即以该连通集合的导出子图的边密度来作为他们的收益系数, 并由此定义了具有边密度的Myerson值, 证明了具有边密度的Myerson值可以由"边密度分支有效性"和"公平性"来唯一确定. 相似文献