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《Discrete Mathematics》2007,307(17-18):2226-2234
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Rudolf Philippe Rohr 《Comptes Rendus Mathematique》2006,342(6):381-385
Let U be a real vector space, B an inner product on U and a 3-form. The 3-form T defines two natural maps, and given by and . We show that is a Lie bracket if and only if is a Lie subalgebra of . To cite this article: R.P. Rohr, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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If is a tree then – T denotes the additive hereditary property consisting of all graphs that does not contain T as a subgraph. For an arbitrary vertex v of T we deal with a partition of T into two trees , , so that , , , , and . We call such a partition a of T. We study the following em: Given a graph G belonging to –T. Is it true that for any -partition , of T there exists a partition of the vertices of G such that and ? This problem provides a natural generalization of Δ-partition problem studied by L. Lovász ([L. Lovász, On decomposition of graphs. Studia Sci. Math. Hungar. 1 (1966) 237–238]) and Path Partition Conjecture formulated by P. Mihók ([P. Mihók, Problem 4, in: M. Borowiecki, Z. Skupien (Eds.), Graphs, Hypergraphs and Matroids, Zielona Góra, 1985, p. 86]). We present some partial results and a contribution to the Path Kernel Conjecture that was formulated with connection to Path Partition Conjecture. 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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Houmem Belkhechine Imed Boudabbous Kaouthar Hzami 《Comptes Rendus Mathematique》2013,351(13-14):501-504
We consider a tournament . For , the subtournament of T induced by X is . An interval of T is a subset X of V such that, for and , if and only if . The trivial intervals of T are ?, and V. A tournament is indecomposable if all its intervals are trivial. For , denotes the unique indecomposable tournament defined on such that is the usual total order. Given an indecomposable tournament T, denotes the set of such that there is satisfying and is isomorphic to . Latka [6] characterized the indecomposable tournaments T such that . The authors [1] proved that if , then . In this note, we characterize the indecomposable tournaments T such that . 相似文献
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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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This paper treats the generalized quantum group with a bi-homomorphism χ for which the corresponding generalized root system is a finite set. We establish a Harish-Chandra type theorem describing the (skew) centers of U. 相似文献