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1.
For a fixed multigraph H with vertices w1,…,wm, a graph G is H-linked if for every choice of vertices v1,…,vm in G, there exists a subdivision of H in G such that vi is the branch vertex representing wi (for all i). This generalizes the notions of k-linked, k-connected, and k-ordered graphs.Given a connected multigraph H with k edges and minimum degree at least two and n7.5k, we determine the least integer d such that every n-vertex simple graph with minimum degree at least d is H-linked. This value D(H,n) appears to equal the least integer d′ such that every n-vertex graph with minimum degree at least d′ is b(H)-connected, where b(H) is the maximum number of edges in a bipartite subgraph of H. 相似文献
2.
For integers , n≥k and r≥s, let m(n,r,s,k) be the largest (in order) k-connected component with at most s colours one can find in any r-colouring of the edges of the complete graph Kn on n vertices. Bollobás asked for the determination of m(n,r,s,k).Here, bounds are obtained in the cases s=1,2 and k=o(n), which extend results of Liu, Morris and Prince. Our techniques use Szemerédi’s Regularity Lemma for many colours.We shall also study a similar question for bipartite graphs. 相似文献
3.
An n-ary operation Q:Σn→Σ is called an n-ary quasigroup of order |Σ| if in the relation x0=Q(x1,…,xn) knowledge of any n elements of x0,…,xn uniquely specifies the remaining one. Q is permutably reducible if Q(x1,…,xn)=P(R(xσ(1),…,xσ(k)),xσ(k+1),…,xσ(n)) where P and R are (n-k+1)-ary and k-ary quasigroups, σ is a permutation, and 1<k<n. An m-ary quasigroup S is called a retract of Q if it can be obtained from Q or one of its inverses by fixing n-m>0 arguments. We prove that if the maximum arity of a permutably irreducible retract of an n-ary quasigroup Q belongs to {3,…,n-3}, then Q is permutably reducible. 相似文献
4.
In this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of the game. Based on the concept of k-additivity, we define the so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities. 相似文献
5.
For integer r≥2, the infinite r-path P∞(r) is the graph on vertices …v−3,v−2,v−1,v0,v1,v2,v3… such that vs is adjacent to vt if and only if |s−t|≤r−1. The r-path on n vertices is the subgraph of P∞(r) induced by vertices v0,v1,v2,…,vn−1. For non-negative reals x1 and x2, a λx1,x2-labeling of a simple graph G is an assignment of non-negative reals to the vertices of G such that adjacent vertices receive reals that differ by at least x1, vertices at distance two receive reals that differ by at least x2, and the absolute difference between the largest and smallest assigned reals is minimized. With λx1,x2(G) denoting that minimum difference, we derive λx1,x2(Pn(r)) for r≥3, 1≤n≤∞, and . For , we obtain upper bounds on λx1,x2(P∞(r)) and use them to give λx1,x2(P∞(r)) for r≥5 and . We also determine λx1,x2(P∞(3)) and λx1,x2(P∞(4)) for all . 相似文献
6.
Let be any atomless and countably additive probability measure on the product space with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset such that can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps simple and continuous functions on to their restrictions to T. 相似文献
7.
The well-known “Bernstein’s weighted problem” deals with the possibility of weighted approximation on the whole real line. In this paper, we show the possibility of k-monotone approximation on the real line with Freud’s weight . 相似文献
8.
For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn, let be the family of all fuzzy sets ofRn, which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space with the topology of endograph metric is homeomorphic to the Hilbert cube Q=[-1,1]ω iff Y is compact; and the space is homeomorphic to {(xn)Q:sup|xn|<1} iff Y is non-compact and locally compact. 相似文献
9.
Let G be an edge weighted graph with n nodes, and let A(3,G) be the average weight of a triangle in G. We show that the number of triangles with weight at most equal to A(3,G) is at least (n−2) and that this bound is sharp for all n≥7. Extensions of this result to cliques of cardinality k>3 are also discussed. 相似文献
10.
In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).