Báo cáo toán học: "Vector spaces and the Petersen graph" pdf

... circuits and G is not ordinary. ✷ Theorem 4.3 If neither G[X] nor G[X] is bipartite, then G is not ordinary. Proof: By hypothesis, b(G) + p(G) ≥ 2, and so the result follows from Theorem 2.3. ✷ The ... 1-factors.) In the next section we derive the existence or otherwise of the set S described earlier by relating the dimensions of the spaces L(G), C(G), E(G) and A(G). 2 A...

Ngày tải lên: 07/08/2014, 15:22

... S and S  merge A, or both S and S  merge B, then, by Theorem 2.2, (ii) holds. Furthermore, making use of the note, the argument for the case that one of the sequences, S say, merges A and the ... V with the property that if e and f are distinct edges of G with the same colour, then at most one of these edges is incident with a vertex in U. The unification of the ver...

Ngày tải lên: 07/08/2014, 21:20

... closed, and convex subsets of the bounded and convex set coC, then µ(C n ) = 0 (n ∈ N), and therefore C ∞ = ∅. Appealing again to the ˇ Smulian theorem [6, Theorem V.6.2] we find that the convex ... denotes the closed and convex hull of A and H(C, D) is the Hausdorff-Pompeiu distance between the bounded subsets C and D of X. The E-L measure of nonconvexity was introdu...

Ngày tải lên: 20/06/2014, 20:20

... are preserved through the mapping, the stable region always lies to the left of the contour. In the v- plane, this is the region above the top horizontal line, and below the lower h orizontal 0 ... Cleveland, OH 44135, USA Authors’ contributions TH and CL worked together in the derivation of the mathematical results. Both authors read and approved the final manuscr...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... Find whether G 1 and G 2 have orthogonal Euler tours. If G 1 and G 2 are equal to the graph G of Problem 1.7 and each directed transition of G has the same colour in G 1 and G 2 , then T 1 and T 2 are ... 2-matroids Let Q 1 and Q 2 be 2-matroids. When Q 1 and Q 2 have the same ground-set and skew classes we shall use Q 1 + Q 2 to denote the parity system which is the...

Ngày tải lên: 07/08/2014, 06:20

... asymptotic formula for f nk from theorem 1.1, together with standard results from random matrix theory relating the behavior of the eigenvalues of random unitary matrices to the behavior of the eigenvalues of ... D 1 be the following operation on tableaux: delete the top-left element of the tableaux, then move the lesser of the element immediately below and the element i...

Ngày tải lên: 07/08/2014, 06:22