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221.
A biclique of a graph G is a maximal induced complete bipartite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1,?1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, ?1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in similar terms as those employed in Gilmore's characterization of clique matrices. On the other hand, the biclique graph of a graph is the intersection graph of the bicliques of G. Using the concept of biclique matrices, we describe a Krausz‐type characterization of biclique graphs. Finally, we show that every induced P3 of a biclique graph must be included in a diamond or in a 3‐fan and we also characterize biclique graphs of bipartite graphs. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 1–16, 2010 相似文献
222.
Given two nonnegative integers s and t, a graph G is (s,t)-supereulerian if for any disjoint sets X,Y⊂E(G) with |X|≤s and |Y|≤t, there is a spanning eulerian subgraph H of G that contains X and avoids Y. We prove that if G is connected and locally k-edge-connected, then G is (s,t)-supereulerian, for any pair of nonnegative integers s and t with s+t≤k−1. We further show that if s+t≤k and G is a connected, locally k-edge-connected graph, then for any disjoint sets X,Y⊂E(G) with |X|≤s and |Y≤t, there is a spanning eulerian subgraph H that contains X and avoids Y, if and only if G−Y is not contractible to K2 or to K2,l with l odd. 相似文献
223.
224.
We show that solutions of the chemical reaction-diffusion system associated to \(A+B\rightleftharpoons C\) in one spatial dimension can be approximated in \(L^2\) on any finite time interval by solutions of a space discretized ODE system which models the corresponding chemical reaction system replicated in the discretization subdomains where the concentrations are assumed spatially constant. Same-species reactions through the virtual boundaries of adjacent subdomains lead to diffusion in the vanishing limit. We show convergence of our numerical scheme by way of a consistency estimate, with features generalizable to reaction networks other than the one considered here, and to multiple space dimensions. In particular, the connection with the class of complex-balanced systems is briefly discussed here, and will be considered in future work. 相似文献
225.
Acta Mathematicae Applicatae Sinica, English Series - Let H = (V, E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the... 相似文献
226.
We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrix-valued RBFs. 相似文献
227.
Group Chromatic Number of Graphs without K5-Minors 总被引:2,自引:0,他引:2
Let G be a graph with a fixed orientation and let A be a group. Let F(G,A) denote the set of all functions f: E(G) ↦A. The graph G is A
-colorable if for any function f∈F(G,A), there is a function c: V(G) ↦A such that for every directed e=u
v∈E(G), c(u)−c(v)≠f(e). The group chromatic numberχ1(G) of a graph G is the minimum m such that G is A-colorable for any group A of order at least m under a given orientation D.
In [J. Combin. Theory Ser. B, 56 (1992), 165–182], Jaeger et al. proved that if G is a simple planar graph, then χ1(G)≤6. We prove in this paper that if G is a simple graph without a K
5-minor, then χ1(G)≤5.
Received: August 18, 1999 Final version received: December 12, 2000 相似文献
228.
Konstantin Mischaikow Harumi Hattori 《Journal of Dynamics and Differential Equations》1990,2(2):163-175
We consider the questions related to the structure of shock waves for a system of magnetohydrodynamic equations. Using Conley's connection matrix, we recover and extend earlier results due to C. Conley and J. Smoller. In particular, we give a simpler proof of the existence of fast and slow shocks with structure. We also demonstrate that for some viscosity parameters intermediate shocks occur. Furthermore, under an assumption of transversality, we show that there exist multi-parameter families of these intermediate shocks.This research was done while both authors were visiting the Lefschetz Center for Dynamical Systems at Brown University.Supported in part by the NSF under Grant DMS-8507056.Supported in part by AFOSR 87-0347. 相似文献
229.
230.
Cyclic curves, i.e. curves fixed by a cyclic collineation group, play a central role in the investigation of cyclic arcs in Desarguesian projective planes. In this paper, the genus of a cyclic curve arising from a cyclic k-arc of Singer type is computed. 相似文献