Báo cáo toán học: "Irregularity strength of regular graphs" potx

... properties of the classified one-factorizations are also tabulated. 1 Introduction An r-factor of a graph G is an r -regular spanning subgraph of G.Anr-factorization of G is a partition of the edges of ... one-factorization of type 4 + 4 + 4 is only possible for three graphs of order 12: the disjoint union of three copies of C 4 , the disjoint union of three copies of...

Ngày tải lên: 07/08/2014, 08:22

... matchings in  -regular graphs Noga Alon ∗ School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540 and Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel ... The solution of the van der Waerden problem for permanents, Dokl. Akad. Nauk SSSR 258 (1981), 1041-1044. [4] D. I. Falikman, A proof of van der Waerden’s conjecture on the pe...

Ngày tải lên: 07/08/2014, 06:22

... monotonicity of f(δ) in the required range, and completes the proof of the theorem. ✷ References [1] A. Alon, S. Hoory, N. Linial, A Continuous Analogue of the Girth Problem, Journal of Combinatorial ... electronic journal of combinatorics 14 (2007), #N1 4 Maximum matchings in regular graphs of high girth Abraham D. Flaxman Microsoft Research Redmond, Washington, USA abie@micros...

Ngày tải lên: 07/08/2014, 13:21

... Subsquares of N 2 squares of order 9. In particular we note that there are 1589 main classes of N ∞ squares of order 9, yet only 37 of these contain pan-Hamiltonian squares. In terms of reduced ... have a generalisation of Lemma 4. §6. Small orders For n ∈{2, 3, 5} thecatalogueofLatinsquaresin[5]showsthatthereisasinglemain class of N ∞ square of order n,namelythatofC n . Acc...

Ngày tải lên: 07/08/2014, 06:20

... sequence of types of the positions wi for i ≥ 1 (we think of this as the right phase diagram of w.) Proposition 4 The right phase diagram of w consists either of : • a string (possibly empty) of N ... full phase diagram of w which consists of the types of all the strings of the form awb where a, b > 0. We write this diagram as a quarter infinite array, with the value...

Ngày tải lên: 07/08/2014, 06:23

... member of the second coordinate of the label of y, delete the edge x j y.If the digit of z is 3 and y is not a member of the second coordinate of the label of z, delete the electronic journal of ... Subclaims, the proof of our lemma is complete. 5 Proof of the Main Theorem In this section, we present the proof of the main theorem. Let C be a topologically closed class o...

Ngày tải lên: 07/08/2014, 06:23

... ordering of the vertices to an ordering of the edges lexicographically. A broken circuit of H ⊆ G is a set of edges B ⊆ H such that there is some edge e ∈ G, smaller than every edge of B, such ... consists of all edges of G with both ends in S. We will use the symbols π and σ to denote set partitions. The notation π  S means π is a set partition of the set S. The length (numb...

Ngày tải lên: 07/08/2014, 08:22

... each face boundary of K 4 and changing the parity of the lengths of the paths of J corresponding to the chosen edges. The set of chosen edges of K 4 is a non-empty cocycle of K 4 since the face ... G. If H is a subgraph of the embedded graph, then H ∗ is the subgraph of G ∗ consisting of the dual edges of H. A bond of G is the minimal nonempty edge cut. To each bond o...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 10 (2003), #R11 10 Proof: Let S = {x 1 ,x 2 , ··· ,x k } be an ordered subset of the vertices of G.LetC be a cycle of maximum order 2c containing all vertices of S in ... contradiction to the above inequality. Let c be the number of elements of S that are not vertices on any of the k + t edges of the matching. Then t + d + c of the edges are free....

Ngày tải lên: 07/08/2014, 07:21

Ngày tải lên: 05/08/2014, 15:21