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1.
Edge Coloring of Embedded Graphs with Large Girth   总被引:3,自引:0,他引:3  
Let G be a simple graph embedded in the surface of Euler characteristic ()0. Denote e(G), and g the edge chromatic number, the maximum degree and the girth of the graph G, respectively. The paper shows that e(G)= if 5 and g4, or 4 and g5, or 3 and g9. In addition, if ()>0, then e(G)= if 3 and g8. Acknowledgments.The authors would like to thank Dr. C.Q. Zhang for carefully reading several versions of this paper during its preparation and for suggesting several stylistic changes that have improved the overall presentation.  相似文献
2.
Sparse PCA by iterative elimination algorithm   总被引:1,自引:0,他引:1  
In this paper we proposed an iterative elimination algorithm for sparse principal component analysis. It recursively eliminates variables according to certain criterion that aims to minimize the loss of explained variance, and reconsiders the sparse principal component analysis problem until the desired sparsity is achieved. Two criteria, the approximated minimal variance loss (AMVL) criterion and the minimal absolute value criterion, are proposed to select the variables eliminated in each iteration. Deflation techniques are discussed for multiple principal components computation. The effectiveness is illustrated by both simulations on synthetic data and applications on real data.  相似文献
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The reachability r(D) of a directed graph D is the number of ordered pairs of distinct vertices (x,y) with a directed path from x to y. Consider a game associated with a graph G=(V,E) involving two players (maximizer and minimizer) who alternately select edges and orient them. The maximizer attempts to maximize the reachability, while the minimizer attempts to minimize the reachability, of the resulting digraph. If both players play optimally, then the reachability is fixed. Parameters that assign a value to each graph in this manner are called competitive parameters. We determine the competitive-reachability for special classes of graphs and discuss which graphs achieve the minimum and maximum possible values of competitive-reachability.  相似文献
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It is known that there are class two graphs with Δ=6 which can be embedded in a surface Σ with Euler characteristic χ(Σ)?0. However, it is unknown whether there are class two graphs on the projective plane or on the plane with Δ=6. In this paper, we prove that every graph with Δ=6 is class one if it can be embedded in a surface with Euler characteristic at least -3 and is C3-free, or C4-free or if it can be embedded in a surface with Euler characteristic at least -1 and is C5-free. This generalizes Zhou's results in [G. Zhou, A note on graphs of class I, Discrete Math. 263 (2003) 339-345] on planar graphs.  相似文献
9.
Rong Luo  Yue Zhao 《Discrete Mathematics》2006,306(15):1788-1790
In 1968, Vizing conjectured that, if G is a Δ-critical graph with n vertices, then α(G)?n/2, where α(G) is the independence number of G. In this note, we verify this conjecture for n?2Δ.  相似文献
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It is proved in this paper that every bipartite graphic sequence with the minimum degree 2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture originally proposed by Keedwell (1993) and reproposed by Cameron (1999) about simultaneous edge-colorings and critical partial Latin squares.* Partially supported by RGC grant HKU7054/03P. Partially supported by the National Security Agency under Grants MDA904-00-1-00614 and MDA904-01-1-0022.  相似文献
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