共查询到20条相似文献,搜索用时 31 毫秒
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For some a and b positive rational numbers, a simple graph with n vertices and edges is an -linear graph, when . We characterize non-empty classes of -linear graphs and determine those which contain connected graphs. For non-empty classes, we build sequences of -linear graphs and sequences of connected -linear graphs. Furthermore, for each of these sequences where every graph is bounded by a constant, we show that its correspondent sequence of diameters diverges, while its correspondent sequence of algebraic connectivities converges to zero. 相似文献
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For a given graph G and a positive integer r the r-path graph, , has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length , and their union forms either a cycle or a path of length in G. Let be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of . The k-history is a subgraph of G that is induced by all edges that take part in the recursive definition of H. We present some general properties of k-histories and give a complete characterization of graphs that are k-histories of vertices of 2-path graph operator. 相似文献
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Let R, S and T be finite sets with , and . A code with covering radius 1 and minimum distance 2 is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality . These bounds turn out to be best possible in many instances. Focussing on the special case we determine when r divides s, when , when s is large, relative to r, when r is large, relative to s, as well as . Finally, a table with bounds on is given. 相似文献
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We study set-theoretic solutions of the Yang–Baxter equations on a set X in terms of the induced left and right actions of X on itself. We give a characterisation of involutive square-free solutions in terms of cyclicity conditions. We characterise general solutions in terms of abstract matched pair properties of the associated monoid and we show that r extends as a solution on as a set. Finally, we study extensions of solutions both directly and in terms of matched pairs of their associated monoids. We also prove several general results about matched pairs of monoids S of the required type, including iterated products equivalent to a solution, and extensions . Examples include a general ‘double’ construction and some concrete extensions, their actions and graphs based on small sets. 相似文献
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A.J.W. Hilton 《Discrete Mathematics》2008,308(5-6):645-669
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In this paper, we give sufficient conditions for a graph to have degree bounded trees. Let G be a connected graph and . We denote by the minimum value of the degree sum in G of any k pairwise nonadjacent vertices of A, and by the number of components of the subgraph of G induced by . Our main results are the following: (i) If , then G contains a tree T with maximum degree ⩽k and . (ii) If , then G contains a spanning tree T with for any . These are generalizations of the result by S. Win [S. Win, Existenz von Gerüsten mit Vorgeschriebenem Maximalgrad in Graphen, Abh. Math. Seminar Univ. Humburg 43 (1975) 263–267] and degree conditions are sharp. 相似文献
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A graph G on n vertices is a tight distance graph if there exists a set such that and if and only if . A characterization of the degree sequences of tight distance graphs is given. This characterization yields a fast method for recognizing and realizing degree sequences of tight distance graphs. 相似文献
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The Cauchy-Davenport theorem states that, if p is prime and A, B are nonempty subsets of cardinality r, s in , the cardinality of the sumset is bounded below by ; moreover, this lower bound is sharp. Natural extensions of this result consist in determining, for each group G and positive integers , the analogous sharp lower bound, namely the function Important progress on this topic has been achieved in recent years, leading to the determination of for all abelian groups G. In this note we survey the history of earlier results and the current knowledge on this function. 相似文献
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Rubén A. Hidalgo 《Journal of Pure and Applied Algebra》2018,222(12):4173-4188
Let p be a prime integer and let be an integer so that . We show that a closed Riemann surface S of genus has at most one p-group H of conformal automorphisms so that has genus zero and exactly r cone points. This, in particular, asserts that, for and , the minimal field of definition of S coincides with that of . Another application of this fact, for the case that S is pseudo-real, is that must be either trivial or a cyclic group and that r is necessarily even. This generalizes a result due to Bujalance–Costa for the case of pseudo-real cyclic p-gonal Riemann surfaces. 相似文献
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We study vertex partitions of graphs according to their Colin de Verdiere parameter μ. By a result of Ding et al. [DOSOO] we know that any graph G with admits a vertex partition into two graphs with μ at most . Here we prove that any graph G with admits a vertex partition into three graphs with μ at most . This study is extended to other minor-monotone graph parameters like the Hadwiger number. 相似文献
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We consider a real Gaussian process X with unknown smoothness where the mean-square derivative is supposed to be Hölder continuous in quadratic mean. First, from the discrete observations , we study reconstruction of , , with , a piecewise polynomial interpolation of degree . We show that the mean-square error of interpolation is a decreasing function of r but becomes stable as soon as . Next, from an interpolation-based empirical criterion, we derive an estimator of and prove its strong consistency by giving an exponential inequality for . Finally, we prove the strong convergence of toward with a similar rate as in the case ‘ known’. To cite this article: D. Blanke, C. Vial, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献