| 词汇 | example_english_graph |
| 释义 | Examples of graphThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. Figure 10(b), (c) shows the possible continuation of those graphs. Nevertheless, it seems likely that the results proved in this paper for huge graphs remain true for graphs of much more modest size. There are no such o simple formulas known for general outerplanar graphs. In this paper, we investigate results of the same type, which are known as splitter theorems, for cubic graphs. Let us first introduce the smallest cubic graphs, the only two on two vertices. The class of graphs which attain this bound is characterised. We close this section with some remarks concerning other base graphs. The second theme is to illustrate the use of induction in proving such results about graphs and matroids. The class of graphs with tree-width at most three requires four excluded minors [1]. We introduce new operations, particular for the class of graphs with path-width at most two. In many instances (such as undirected graphs and other symmetric relations) this is also a natural definition of a subobject. However, this is not possible in the unimodular case of unweighted graphs. The example in the immediately preceding paragraph shows that such graphs exist. Here we will need a slight extension of that result, assuming that only two out of the three bipartite graphs are -regular. The properties of such graphs in which is much smaller than d have been studied extensively. Most other parts of the tree proof are also inadequate, but can be replaced by more complicated arguments which suffice for the more complex graphs. The concept of minimally k -connected graphs is helpful in proving the following. Series-parallel graphs are in general loopless multigraphs, and are planar. Research on circle graphs includes a complete a characterization and a polynomial time algorithm for identifying them. On the other hand, there exist polynomial algorithms to solve instances of this problem in cubic graphs [13], permutation graphs [14] and interval graphs [15]. To be exact, the list does not contain all such graphs, but they are ordered to subgraph chains and only the minimal elements are taken. We generalize this result to graphs with arbitrarily large girth. The most interesting and well-studied type of degree-restricted graphs, owing to stability in the natural setting, are the regular graphs. In this paper we consider an asymptotic behaviour of the choice number of random graphs. Both papers also give upper bounds for the choice number of pseudo-random graphs. We will now characterize the triangle-free graphs that have a unique closure (in the labelled sense) via their dist-2-graphs. Moreover, much information is presented only in the form of graphs, and these also provide no indication of number of cases. We also require that the walks take place on graphs that are strong expanders. Many graphs can be generated by a multiset, but one clearly sees that these graphs are isomorphic. The twisted odd graphs are obtained from the well-known odd graphs through an involutive automorphism. As some simple consequences of our regular partition and such general results, we can derive, for instance, the following properties of the twisted odd graphs. Nevertheless, this negative result can be circumvented for certain classes of graphs. One of the main ideas we shall use is to consider weighted random graphs. Finally, we have considered random geometric graphs in the subcritical regime. In fact, the weighted graphs can be thought of as a convenience, which is probably not an essential part of the proof. We provide an alternate proof of the central limit theorem for the fluctuations of the size of the giant component in sparse random graphs. To make the question more precise we need to decide on what kind of random graphs we wish to consider. As a matter of fact, most of the common special cases of graphs are artificial in this sense. The following strengthening is a powerful general tool for embedding bounded degree graphs (and often trees, too). Therefore, vertex-triads in matroids are direct generalizations of vertices of degree three in 3-connected graphs. We now consider some other specific families of graphs closed under minors. To determine the number of graphs with exactly one cycle, we proceed as follows. Unfortunately, the number of equations is extremely large for complete graphs. Regarding mixing for random walks on other models of random graphs, see [6], [13] and [8]. The colour classes corresponding to chromatic number are the colour classes determined by complete graphs. One difficulty seems to be that there are several graphs of different structure for which there is equality in (5). Exactly the same modification as that for the main algorithm must be made to cope with non-simple graphs. The main result of the paper is that for many important properties there are exactly two boundary classes of planar graphs. Thus, in many respects, planar graphs are difficult, but not all of them. Moreover, we will show that all these parameters are unbounded for line graphs of bounded vertex degree. In this note we point out that, as far as sparse random graphs are concerned, these two perspectives actually arrive at the same answer. Indeed, according to [4], for planar graphs, tree-width is bounded if and only if clique-width is bounded. Let us now return to the question of a 'spectral theory' for bipartite graphs. In this paper, we describe an infinite, nontrivial class of graphs and matroids for which a generalized version of both conjectures holds. There is no need to restrict ourselves to graphs. One way to prove lower bounds for the expansion rate of symmetrical graphs is based on the enumeration of geodesics. We are now ready to define random intersection graphs. The trick here is to 'divide and conquer', which was applied earlier for random graphs in [4]. Permutations, mappings and 2-regular graphs are all logarithmic assemblies. We note that a special case of this version (for embedding graphs of maximum degree three) appeared in [8]. The problem can be reformulated in the following way in terms of graphs. We consider random graphs with a fixed degree sequence. By now we know much about the structure of random regular graphs. To achieve symmetry, we thus need that the class of graphs satisfying () is closed under taking duals. We mention one fact about this order for graphs. Finally, we use the method of -nets to improve the known bounds on the edge expansion of random d-regular graphs. The robustness of these graphs has been studied experimentally in [3], heuristically in [13, 14] and rigorously in [8]. Their first step was to prove the following simple-looking statement about graphs. The remaining graphs show that the range of generalization decreases as a function of the number of examples. The following two propositions expose some general properties of thinned-out graphs. Whereas for thinned-out graphs (unbounded lengthdifferences) they have to respect simple walks, as we will see below. In particular, it does not have any invariant graphs. We will usually not distinguish between invariant graphs as functions and as point sets. The correct definition of row-finiteness for topological graphs may be the following. In this paper, we unify the two analyses of ideal structures, and generalize them to the setting of topological graphs. More examples of this case and of cases (b1) and (b2) are easily constructed by labeling infinite graphs. The text is very well illustrated, the large format being exploited to provide clear diagrams and graphs. There is some sort of illustration, ranging from full colour photos and maps to black-and-white graphs and diagrams. The graphs obtained from the numerical integration of the partial differential equations do not have this feature. Uniformly finite-to-one and onto extensions of homomorphisms between strongly connected graphs. From these results, points for zero diameter ratio could be added to the graphs ofrelative error against diameter ratio. Vertical bars are the standard error in both graphs. Regular networks and random graphs have been considered as models to describe the topology of most systems for a long time. If b is consistently small, then fewer candidate graphs will be accepted, and the effective number of samples will be reduced. Note that the scale is different for the two variance graphs. The ' rightmost ' intersection of the graphs of the lefthand and right-hand sides of (70) defines the relevant equilibrium of the model. Tables, graphs, and figures need to be placed on individual pages. Randomly selected representatives of graphs do not incorporate semantics and ease of interpretation based on user interests. We created five graphs, each having two circles. The vertical scale on the graphs indicates the percentage of building area and the horizontal the lifetime duration of a building, or group of buildings. We begin by describing the graphical technique and then move on to the various measures that can be derived from these graphs for statistical analysis. There was generally good correspondence between the two linkage methods in terms of morphology of the graphs and phenotypes showing linkage. We will use the efficient rabbit strategy for cycles as a subroutine on graphs with arbitrary diameter. He even observes that this can be reduced further because regular graphs of odd order and odd degree don't exist! Local communication in the radio model was considered in for arbitrary graphs, under the name single round simulation. The graphs we are interested in are defined on some kind of metric space. In this paper we study eigenvalues of random graphs. By applying our main theorem we can obtain the following result about the connectivity threshold for vertex-transitive graphs. First, it gives a fairly general sufficient condition for a family of graphs to satisfy the sharp threshold property. Our general hunter strategy is based on a hunter strategy for cycles which is then simulated on general graphs. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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